JJ BvB, facing lots of aggression

in higher limits... "standard" play is indeed a pretty easy 5betship, and as played this is a dream flop because you pretty much only lose to higher overpairs while all overcards/random sc whiff. so, easy get it in.

however, this is nl2, so your assumption that villain only 4bets QQ+ and AK might be true.
if that happens to be his range, the best play should be to 3bet/fold, assuming that he will call some worse hands and only 4bet with better.

but you don't actually know what is his range, of course.
on nl2 without ANY info, i'd probably get it in because who knows what he might be doing, but wouldn't be too happy about it.
any piece of info you can get in the player can help with the decision, such as if the player is being tight over a small sample i'd be more inclined to 3bet/fold it, since it's probably some noob following preflop charts and not going to 4bet you wide.

If we want to play solely for setmining we should fold here. When we call we have 30bb left and we are pot committed. Any other card but a J is no good card for shoving IMO

1) this is NL2, so I assume not so many 4bet bluffs
2) hero 3bets BTN quite big, and
3) BB's 4bet is a cold 4bet which makes it look even stronger

I would fold here.