Overpair on a raggedy board

Villain is a bit hard to figure - for 20 hands or so he seemed nitty and had numbers like 11/5/1. Then for the next few orbits he raised a lot preflop, made several preflop 3-bets, and won one big hand. In that, he had suited overcards on a flush draw board - got it all in against a guy with TPTK and ended up hitting his flush.

Don't have the hand history but here's what happened:

I was the CO with a full $50 stack. Villain is the BB and has me covered.
I raise to 1.75 with :Jd: :Jc:. Both blinds call. Pot headed to the flop is 5.25.

Flop - :7s:, :4s:, :2h:

SB checks, villain checks, I bet 5.00, SB folds, villain pushes :shock: .

er?

I'm torn - interested to see what others think. Probably call, but hate myself for paying off a set.

Heavily read-dependent, which in this case makes me want to look him up. You'll see 88-TT, flush draws and oesds a lot here.

Let me ask an auxiliary question: if I have something like :As: :Kh: instead of JJ is this an insta-fold? It would seem superficially awful to call, but if draws and middle pairs are a lot of his range, I am ahead of many of those and have a clutch of outs against the rest. (That's a totally theoretical idea - I don't think I'd ever make that call without a lock read on the guy that said it was superlikely he had a draw and superunlikely he had a set.)

of course AK is a fold here. It's like a SA/WB situation... No way that's profitable in the long run... But as for the JJ my first reaction was snapcall, then it was snapfold and now i am lost too.

So i fold. But tough spot indeed.