Hi  itsme,
Refer below sample.
HTML
<asp:CheckBox ID="mon" Text="Monday" runat="server" /><br />
<asp:CheckBox ID="tues" Text="Tuesday" runat="server" /><br />
<asp:CheckBox ID="wed" Text="Wednesday" runat="server" /><br />
<asp:CheckBox ID="thrus" Text="Thrusday" runat="server" /><br />
<asp:CheckBox ID="fri" Text="Friday" runat="server" /><br />
<asp:CheckBox ID="sat" Text="Saturday" runat="server" /><br />
<asp:CheckBox ID="sun" Text="Sunday" runat="server" /><br />
<asp:GridView runat="server" AutoGenerateColumns="false" ID="gvDays">
    <Columns>
        <asp:TemplateField HeaderText="Days">
            <ItemTemplate>
                <asp:Label ID="lblweeks" runat="server" Text='<%#Eval("Days") %>'></asp:Label>
            </ItemTemplate>
        </asp:TemplateField>
        <asp:TemplateField HeaderText="Edit">
            <ItemTemplate>
                <asp:Button Text="Edit" runat="server" OnClick="Edit" />
            </ItemTemplate>
        </asp:TemplateField>
    </Columns>
</asp:GridView>
Namespaces
C#
using System.Data;
VB.Net
Imports System.Data
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.Add("Days");
        dt.Rows.Add("Monday,Tuesday,Wednesday");
        dt.Rows.Add("Monday,Tuesday,Wednesday,Thrusday");
        dt.Rows.Add("Monday,Thrusday");
        dt.Rows.Add("Tuesday,Sunday");
        gvDays.DataSource = dt;
        gvDays.DataBind();
    }
}
protected void Edit(object sender, EventArgs e)
{
    Button btn = sender as Button;
    GridViewRow row = btn.NamingContainer as GridViewRow;
    string weeks = (row.FindControl("lblweeks") as Label).Text;
    string[] parts1 = weeks.Split(',');
    mon.Checked = false;
    tues.Checked = false;
    wed.Checked = false;
    thrus.Checked = false;
    fri.Checked = false;
    sat.Checked = false;
    sun.Checked = false;
    for (int i = 0; i < parts1.Length; i++)
    {
        if (parts1[i].ToUpper() == "MONDAY")
        {
            mon.Checked = true;
        }
        if (parts1[i].ToUpper() == "TUESDAY")
        {
            tues.Checked = true;
        }
        if (parts1[i].ToUpper() == "WEDNESDAY")
        {
            wed.Checked = true;
        }
        if (parts1[i].ToUpper() == "THRUSDAY")
        {
            thrus.Checked = true;
        }
        if (parts1[i].ToUpper() == "FRIDAY")
        {
            fri.Checked = true;
        }
        if (parts1[i].ToUpper() == "SATURDAY")
        {
            sat.Checked = true;
        }
        if (parts1[i].ToUpper() == "SUNDAY")
        {
            sun.Checked = true;
        }
    }
}
VB.Net
Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        Dim dt As DataTable = New DataTable()
        dt.Columns.Add("Days")
        dt.Rows.Add("Monday,Tuesday,Wednesday")
        dt.Rows.Add("Monday,Tuesday,Wednesday,Thrusday")
        dt.Rows.Add("Monday,Thrusday")
        dt.Rows.Add("Tuesday,Sunday")
        gvDays.DataSource = dt
        gvDays.DataBind()
    End If
End Sub
Protected Sub Edit(ByVal sender As Object, ByVal e As EventArgs)
    Dim btn As Button = TryCast(sender, Button)
    Dim row As GridViewRow = TryCast(btn.NamingContainer, GridViewRow)
    Dim weeks As String = (TryCast(row.FindControl("lblweeks"), Label)).Text
    Dim parts1 As String() = weeks.Split(","c)
    mon.Checked = False
    tues.Checked = False
    wed.Checked = False
    thrus.Checked = False
    fri.Checked = False
    sat.Checked = False
    sun.Checked = False
    For i As Integer = 0 To parts1.Length - 1
        If parts1(i).ToUpper() = "MONDAY" Then
            mon.Checked = True
        End If
        If parts1(i).ToUpper() = "TUESDAY" Then
            tues.Checked = True
        End If
        If parts1(i).ToUpper() = "WEDNESDAY" Then
            wed.Checked = True
        End If
        If parts1(i).ToUpper() = "THRUSDAY" Then
            thrus.Checked = True
        End If
        If parts1(i).ToUpper() = "FRIDAY" Then
            fri.Checked = True
        End If
        If parts1(i).ToUpper() = "SATURDAY" Then
            sat.Checked = True
        End If
        If parts1(i).ToUpper() = "SUNDAY" Then
            sun.Checked = True
        End If
    Next
End Sub
Screenshot
