I personally would just call this turn although there are arguments for shoving... Villain is uncapped and would call our jam quite often with hands that beat us. TT, 89s or 9Ts are the only real hands we can get solid value from. I agree his sizing is weak but he could be trying to keep you in the pot with your marginal holdings on that board pair turn. Also, it's an odd card for him to barrel on, I'd expect a few people to give up this turn but given his aggression, it's not too surprising... But it could still be for value. He may also be barreling FD's like you mentioned

JJ is always really hard to play OOP in a 3bet pot on low boards. I just try to cross my fingers and hold on =/ If we call turn, we'll most likely be calling most river cards, that's why shoving the turn can't be that bad

Tough spot

4 betting JJ pre in the micros is thin, people aren't stacking off much different from QQ+AK hardly ever.

As played I would just call flop and turn, as shoving turn just gets him off his bluffs but better hands aren't folding.

I think you might be a little worried about him 3 barreling you off a better hand with AK AQ type hands, but it won't happen much so don't worry. Against most players I'm still folding this even if the river is a blank such as 3d.