We cannot provide any support whatsoever for the FatFreeCart.com cart -- that's one of the reasons it's free. :^) If you can figure out some way to let PayPal calculate shipping without using PayPal's cart, that would be entirely up to you to set up and troubleshoot.
However, the E-junkie cart (aka "FatFreeCart Pro") has much more flexible built-in Shipping calculation, including actual USPS postal-rate lookups and other, creative approaches like those described here:
http://www.e-junkie.com/ej/help.shipping.htm