You can get checkbox value by alternate way that is, Instead of passing variable value pass the data extension name in the URL. Then read the data extension name as parameter then lookup for checkbox value on your submit page. I am assuming your checkbox type is boolean so the code will be

set @Email = email to match for checkbox value true or false 

set @DE= RequestParameter('Your Data Extenion Name Passed as parameter')

set @value = Lookup(@DE, "checkbox field name", "Email", @Email)

IF @value == True THEN

   Your Code If True

ELSEIF @opt == False THEN

    Your Code If False

ENDIF

You can get checkbox value by alternate way that is, Instead of passing variable value pass the data extension name in the URL. Then read the data extension name as parameter then lookup for checkbox value on your submit page. I am assuming your checkbox type is boolean so the code will be

set @Email = email to match for checkbox value true or false 

set @DE= RequestParameter('Your Data Extenion Name Passed as parameter')

set @value = Lookup(@DE, "checkbox field name", "email", @Email)

IF @value == True THEN

   Your Code If True

ELSEIF @opt == False THEN

    Your Code If False

ENDIF