AJ MP2 flop AQ2 rainbow, call shove on river vs loose player?

Well you don't beat any reasonable value hand, so the question is does he have a bluff often enough here for you to call? I doubt it.

He could easily have AQ/A2/AT/QT/KJ here.

I would check back the turn. I'm not keen on double-barreling with TP. Bet flop, check turn, call river is a standard line here, I believe. As played, you have to fold. You can't base your decision on having seen him overplay one hand.

After T comes in, every reasonable Ax beat you, since you've got a blocker for fd, u don't need to bet in order to protect your hand from oncoming cards

X back turn, call river. As played fold OTT.

Xback turn is right. Any value Ax in his range beat us.
As played we should fold.

Hi,

I'd raise only 3x pre-flop, 4x seems quite much tbh.

Post-flop I'd bet smaller on flop - board is pretty dry, and we are already in wa/wb situation here.

As played, I would have checked turn here - Ax combinations are ahead of use and the only thing you will achieve by betting is to make opponent fold Qx.

Against a Turn raise snap-fold, he should have 0 % bluff-range in this multi-way pot and after you barrel 2 streets.