I really like spenda's idea of 4bet shoving over these 3bets since they are unnecessarily large for the situation. I particularly like the play w/ JJ/QQ since they don't flop an overpair as often and it's more likely to get called by a smaller pair thinking we have 2 big cards like bspahn said.

When someone flats my 4b like this, no matter what the flop is, I just go ahead and bet like 1/4 pot. So pot was 60, I'd bet like 15. If he calls, turn pot size is 90 and effective stacks are 55, I'd bet 20. If he hasn't raised you and hasn't folded by this point, he's trapping you so don't put in the last bet. Obviously this is super exploitable if villain knows what you're doing, but I've been using this with tremendous success, particularly in HU games. The hands people are flatting 4bets with seem to me to be something like 88-TT and AQs/AJs/ATs/KQs. They just fold soso often when I do this that I think it's pretty profitable (obviously I'm gonna change it up when I start feeling like I'm losing in these spots though).