The resale value of your current equipment is roughly half of what you paid for it. There will often be anywhere from a few to a lot of gold coins added to the price the fat man offers you for your weapon. This number is somewhat related to your charm score.
If your charm reaches over 100 points, you will sometimes be offered 2/3 the price of your weapon, rather than slightly over half. Sometimes you will see this same effect if your charm drops below zero--a handy glitch early in the game.
Often, players will (S)ell their weapon, then say no to the offered price several times in succession, in order to get a feel for the range the fat man will offer. Though the difference might only be pocket change, this can be useful in times when you're very tight on money, and still need to upgrade your armor or break into the Inn.