Let me add what I think then.
- You can't run while holding a big gun
Maybe this could depend on strength, or the Weapon Handling perk.
- Big guns could be heavier to avoid characters having 2 bazookas in each hand and a minigun in the mouth.
I don't think this is the right decision, not many people take 2 bazookas with them anyway. Upping the weight would just make them unable to pick up the loot they've earned.
- Rise up the strength requirement to use big guns (ST min 8-9)
Oh man, I hope not, (explained below, SPECIAL point usage problems).
- Rise up the action points we need to shoot (8 Ap instead of 7 Ap for example)
If this ever came to light, no one would pick Big Guns. For the simple reason that you need a high strength in the first place to be able to use them (unless you take Weapon Handling, which mimics +2 Strength). It would simply take too much SPECIAL points in the beginning.
Overall, number 1 seems the most reasonable and understandable.