The code is almost completed. You can also bind properties. So change the XAML to:
<CheckBox Content="" Height="16" HorizontalAlignment="Right" Margin="0,297,118,0" Name="checkBox1" VerticalAlignment="Top"
Command="{Binding CheckCommand, Mode=TwoWay}"
IsChecked="{Binding Path=IsChecked, Mode=TwoWay}">
</CheckBox>
This will bind the IsChecked property of the CheckBox to the IsChecked property of your viewmodel. I have removed the CommandParameter in the Command. You won't need it because in your viewmodel you can use this.IsChecked to get the checked state of the CheckBox.