Cad brings up two points here, both very good ones, one about STR and the other about progressive penalties for recoil.
The Strength requirements for weapons make sense across the board, but there are some glaring exceptions. M16A2 is one example of a poorly statted weapon in Fallout. I trained and qualified with the M16A2, as have hundreds of thousands of U.S. service members over the past 20 years, and my STR is probably only a 4 or so. It weighs about nine pounds loaded and is designed to be very easy to handle. There were those who couldn't qualify on the rifle range, but not because they were too weak to handle the weapon (it was more because they didn't apply the mental discipline to learn basic marksmanship). You can shoot the weapon and do it well without a 6 STR. Likewise there are some small handguns that need a 5 STR and some bigger ones (like the Desert Eagle) that only need a 4, and so on.
As far as penalties for shooting bursts, this is not in the basic PnP rules but I think it was incorporated in Fallout 3. It rears its head in the "Nice Grouping" perk which mentions -4 adn -8 penalties for progressive rounds fired, but that's the only place I have found any mention of burst penalties.
I think a straight -10% penalty for every point of STR you are short of the minimum is reasonable and won't break the game for anyone. Yes, this would mean a guy with 1 STR could pick up and shoot a minigun, but he'd be at a -60 to hit.
