Hi lingers,
Check this example. Now please take its reference and correct your code.
HTML
<div>
    <div id="dialog" style="display: none" align="center">
        <span id="lblMessage"></span>
    </div>
    <asp:GridView ID="avDetails"
        runat="server" AutoGenerateColumns="False" Font-Names="Candara"
        Font-Size="14px" DataKeyNames="pid" Width="24%" Style="margin-bottom: 0px"
        CssClass="grid" CellPadding="2" ForeColor="#333333" GridLines="None" Font-Bold="True"
        OnRowDataBound="OnRowDataBound">
        <AlternatingRowStyle BackColor="White" />
        <Columns>
            <asp:BoundField DataField="id" HeaderText="ID" />
            <asp:BoundField DataField="posino" HeaderText="POSINO" />
            <asp:BoundField DataField="Rev" HeaderText="REV" />
            <asp:BoundField DataField="" HeaderText="STATUS" />
            <asp:TemplateField HeaderText="USE">
                <ItemTemplate>
                    <asp:CheckBox ID="chkSelect" runat="server" OnCheckedChanged="OnChckedChanged" AutoPostBack="True" />
                </ItemTemplate>
            </asp:TemplateField>
        </Columns>
        <EditRowStyle BackColor="#2461BF" />
        <FooterStyle BackColor="#507CD1" Font-Bold="True" ForeColor="White" />
        <HeaderStyle BackColor="#507CD1" Font-Bold="True" ForeColor="White" />
        <PagerStyle BackColor="#2461BF" ForeColor="White" HorizontalAlign="Center" />
        <RowStyle BackColor="#EFF3FB" />
        <SelectedRowStyle BackColor="#D1DDF1" Font-Bold="True" ForeColor="#333333" />
        <SortedAscendingCellStyle BackColor="#F5F7FB" />
        <SortedAscendingHeaderStyle BackColor="#6D95E1" />
        <SortedDescendingCellStyle BackColor="#E9EBEF" />
        <SortedDescendingHeaderStyle BackColor="#4870BE" />
    </asp:GridView>
    <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <link rel="stylesheet" href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8.24/themes/smoothness/jquery-ui.css" />
    <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.8.24/jquery-ui.min.js"></script>
    <script type="text/javascript">
        function ShowPopup(message) {
            $("#lblMessage").html(message);
            $("#dialog").dialog({
                modal: true,
                title: "Message Alert",
                width: 350,
                height: 160
            });
        }
        $(function () {
            $(window).on('popstate', function () {
                $('#myModal').modal('hide');
            });
        });
    </script>
</div>
Namespaces
C#
using System.Configuration;
using System.Data;
using System.Data.SqlClient;
VB.Net
Imports System.Configuration
Imports System.Data
Imports System.Data.SqlClient
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!IsPostBack)
    {
        BindUserDetails1();
    }
}
protected void BindUserDetails1()
{
    string constr1 = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con1 = new SqlConnection(constr1))
    {
        using (SqlDataAdapter sda1 = new SqlDataAdapter("SELECT * from cylinde", con1))
        {
            using (DataTable dt1 = new DataTable())
            {
                sda1.Fill(dt1);
                avDetails.DataSource = dt1;
                avDetails.DataSource = dt1;
                avDetails.DataBind();
            }
        }
    }
}
protected void OnRowDataBound(object sender, GridViewRowEventArgs e)
{
    if (e.Row.RowType == DataControlRowType.DataRow)
    {
        int id = Convert.ToInt32(e.Row.Cells[2].Text);
        string[] cylinders = GetAcceptedCylinder(id.ToString()).Replace("[", "").Replace("]", "").Split(',');
        CheckBox chkSelect = e.Row.FindControl("chkSelect") as CheckBox;
        if (cylinders.Contains("'" + e.Row.Cells[1].Text + "'"))
        {
            chkSelect.Checked = true;
        }
        else
        {
            chkSelect.Checked = false;
        }
        TableCell statusCell = e.Row.Cells[3];
        if (id > 100)
        {
            statusCell.Text = "Used";
        }
        else
        {
            statusCell.Text = "New";
        }
    }
}
protected void OnChckedChanged(object sender, EventArgs e)
{
    CheckBox chk = (CheckBox)sender;
    GridViewRow row = (GridViewRow)chk.NamingContainer;
    string number = row.Cells[1].Text;
    string pid = "206";
    string constring = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constring))
    {
        string acceptedCylinder = GetAcceptedCylinder(pid);
        if (chk.Checked)
        {
            if (acceptedCylinder == "[]")
            {
                using (SqlCommand cmd = new SqlCommand("UPDATE issuesheet SET cylinders = @cylinders where pid='206'", con))
                {
                    cmd.Parameters.AddWithValue("@cylinders", "['" + number.Trim() + "']");
                    con.Open();
                    cmd.ExecuteNonQuery();
                    con.Close();
                }
                ClientScript.RegisterStartupScript(this.GetType(), "Popup", "ShowPopup('Record Inserted successfully.');", true);
            }
            else
            {
                List<string> cylinderNo = acceptedCylinder.Replace("[", "").Replace("]", "").Replace("'", "").Split(',').ToList();
                cylinderNo.Add(number);
                using (SqlCommand cmd = new SqlCommand("UPDATE issuesheet SET cylinders = @cylinders where pid='206'", con))
                {
                    cmd.Parameters.AddWithValue("@cylinders", "['" + string.Join("','", cylinderNo.Distinct()) + "']");
                    con.Open();
                    cmd.ExecuteNonQuery();
                    con.Close();
                }
                ClientScript.RegisterStartupScript(this.GetType(), "Popup", "ShowPopup('Record Updated Successfully.');", true);
            }
        }
        else
        {
            if (!string.IsNullOrEmpty(acceptedCylinder))
            {
                List<string> cylinderNo = acceptedCylinder.Replace("[", "").Replace("]", "").Replace("'", "").Split(',').ToList();
                cylinderNo.Remove(number);
                using (SqlCommand cmd = new SqlCommand("UPDATE issuesheet SET cylinders = @cylinders where pid='206' ", con))
                {
                    cmd.Parameters.AddWithValue("@cylinders", cylinderNo.Distinct().Count() > 0 ? "['" + string.Join("','", cylinderNo.Distinct()) + "']" : "[]");
                    con.Open();
                    cmd.ExecuteNonQuery();
                    con.Close();
                }
                ClientScript.RegisterStartupScript(this.GetType(), "Popup", "ShowPopup('Record Deleted Successfully.');", true);
            }
        }
    }
}
private string GetAcceptedCylinder(string pid)
{
    string acceptCylinder = "";
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand())
        {
            cmd.CommandText = "SELECT cylinders FROM issuesheet WHERE pid=@pid ";
            cmd.Connection = con;
            cmd.Parameters.AddWithValue("@pid", 206);
            con.Open();
            acceptCylinder = Convert.ToString(cmd.ExecuteScalar());
            con.Close();
        }
    }
    return acceptCylinder;
}
VB.Net
Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not IsPostBack Then
        BindUserDetails1()
    End If
End Sub
Protected Sub BindUserDetails1()
    Dim constr1 As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con1 As SqlConnection = New SqlConnection(constr1)
        Using sda1 As SqlDataAdapter = New SqlDataAdapter("SELECT * from cylinde", con1)
            Using dt1 As DataTable = New DataTable()
                sda1.Fill(dt1)
                avDetails.DataSource = dt1
                avDetails.DataSource = dt1
                avDetails.DataBind()
            End Using
        End Using
    End Using
End Sub
Protected Sub OnRowDataBound(ByVal sender As Object, ByVal e As GridViewRowEventArgs)
    If e.Row.RowType = DataControlRowType.DataRow Then
        Dim id As Integer = Convert.ToInt32(e.Row.Cells(2).Text)
        Dim cylinders As String() = GetAcceptedCylinder(id.ToString()).Replace("[", "").Replace("]", "").Split(","c)
        Dim chkSelect As CheckBox = TryCast(e.Row.FindControl("chkSelect"), CheckBox)
        If cylinders.Contains("'" & e.Row.Cells(1).Text & "'") Then
            chkSelect.Checked = True
        Else
            chkSelect.Checked = False
        End If
        Dim statusCell As TableCell = e.Row.Cells(3)
        If id > 100 Then
            statusCell.Text = "Used"
        Else
            statusCell.Text = "New"
        End If
    End If
End Sub
Protected Sub OnChckedChanged(ByVal sender As Object, ByVal e As EventArgs)
    Dim chk As CheckBox = CType(sender, CheckBox)
    Dim row As GridViewRow = CType(chk.NamingContainer, GridViewRow)
    Dim number As String = row.Cells(1).Text
    Dim pid As String = "206"
    Dim constring As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con As SqlConnection = New SqlConnection(constring)
        Dim acceptedCylinder As String = GetAcceptedCylinder(pid)
        If chk.Checked Then
            If Equals(acceptedCylinder, "[]") Then
                Using cmd As SqlCommand = New SqlCommand("UPDATE issuesheet SET cylinders = @cylinders where pid='206'", con)
                    cmd.Parameters.AddWithValue("@cylinders", "['" & number.Trim() & "']")
                    con.Open()
                    cmd.ExecuteNonQuery()
                    con.Close()
                End Using
                ClientScript.RegisterStartupScript([GetType](), "Popup", "ShowPopup('Record Inserted successfully.');", True)
            Else
                Dim cylinderNo As List(Of String) = acceptedCylinder.Replace("[", "").Replace("]", "").Replace("'", "").Split(","c).ToList()
                cylinderNo.Add(number)
                Using cmd As SqlCommand = New SqlCommand("UPDATE issuesheet SET cylinders = @cylinders where pid='206'", con)
                    cmd.Parameters.AddWithValue("@cylinders", "['" & String.Join("','", cylinderNo.Distinct()) & "']")
                    con.Open()
                    cmd.ExecuteNonQuery()
                    con.Close()
                End Using
                ClientScript.RegisterStartupScript([GetType](), "Popup", "ShowPopup('Record Updated Successfully.');", True)
            End If
        Else
            If Not String.IsNullOrEmpty(acceptedCylinder) Then
                Dim cylinderNo As List(Of String) = acceptedCylinder.Replace("[", "").Replace("]", "").Replace("'", "").Split(","c).ToList()
                cylinderNo.Remove(number)
                Using cmd As SqlCommand = New SqlCommand("UPDATE issuesheet SET cylinders = @cylinders where pid='206' ", con)
                    cmd.Parameters.AddWithValue("@cylinders", If(cylinderNo.Distinct().Count() > 0, "['" & String.Join("','", cylinderNo.Distinct()) & "']", "[]"))
                    con.Open()
                    cmd.ExecuteNonQuery()
                    con.Close()
                End Using
                ClientScript.RegisterStartupScript([GetType](), "Popup", "ShowPopup('Record Deleted Successfully.');", True)
            End If
        End If
    End Using
End Sub
Private Function GetAcceptedCylinder(ByVal pid As String) As String
    Dim acceptCylinder As String = ""
    Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con As SqlConnection = New SqlConnection(constr)
        Using cmd As SqlCommand = New SqlCommand()
            cmd.CommandText = "SELECT cylinders FROM issuesheet WHERE pid=@pid "
            cmd.Connection = con
            cmd.Parameters.AddWithValue("@pid", 206)
            con.Open()
            acceptCylinder = Convert.ToString(cmd.ExecuteScalar())
            con.Close()
        End Using
    End Using
    Return acceptCylinder
End Function
Screenshot
