I think that I'm understanding what is going on. It looks like you are passing the size to the cart ok but on the cart page you just have the same size select list. The problem with this is that there is nothing to set the value of the select list you have in the cart. The value that you are submitting for the size is effectively being ignored. To test this part out you should update the cart display that you have. Instead of having the select list here you should just have this column display the cart column for size from the bindings.
This will let you know if the size is getting passed to the cart. Getting a select list to be set to the value of the selected size for that item will not be an easy thing. How do you get the select list to reflect the current size? You have the option to set the select list to a dynamic value but you will need to make it set to the value for that item. This part would require some custom coding on the cart display page.