You would need to have a cart column for the weight (by default, a Weight column is created), and in the add to cart button, set the weight for each item
then you would need to create a recordset that filters the tables based on the shipping country selected on the checkout page, (Shipping county should be stored in a session, so use that in the recordset) and the total weight.
you can return the total weight using
Save the value returned by the recordset into a session variable.
and use that session in the shipping calculation.