For checkbox input the important attributes are:
<input type="checkbox" name="cb_name" value="cb_val" checked="checked" />
When the form is submitted, the value of cb_name will be cb_val whatever its value if the checkbox is checked, if it is not checked then cb_val will not even be set.
Now you can figure out where to put your if(isset(...)) code, instead of in the value attribute it should be outside of it.
<input type="checkbox" name="cb_name" value="1" <?php if ($cb_name == 1) echo 'checked="checked"' ?> />
or if you're using laravel blade template:
<input type="checkbox" name="cb_name" value="1" @if($cb_name == 1) checked="checked" @endif />