if you want the user to uncheck the box being already checked, once the user submits the form, you have to set the value of the cookie of this particular user to be equal to "false", that way it will not be checked again when the page is loaded dynamically. (i assume the value of the cookie was equal to true before)
note: if you have more than one check boxes, each cookie should be associated with each box.
surely if the user tries to uncheck the box, you could unset() the variable. This would allow the box to be unchecked. I'm not sure about the rest of your code and whether this will fit in, but it will probably work in this case.