That's not possible due to security reasons. A checkbox list has pre-defined options; user cannot modify them. Therefore, you cannot use a Client Side action to change the values.
Let's say you were selling something for $200; any clever user would be able to change the value to $2 using JavaScript. Hence, the values are not saved.
You can only change the values on client side for fields that allow user input such as a textbox.
You must bind the Checkbox at server side. Try the "Update multiple form fields by executing a SQL Query". That is executed server side.