Quick question here: Should I bet the turn?

Against his opening size, I only call AJo in the BB. Most of the time, against other opening sizes it's a 3bet.

Flop call is easy, but should I bet the turn myself?
Villain is on the looser side, but not completely off the charts.
He is also cbetting 83% on a 500 hands sample.

He probably has a lot of air on the turn and hands with vulnerable SDV.

Does it make sense to bet this turn for protection?
The 8d strengthens both of our ranges and he can pick up a diamond FD though so maybe not enough FE?
But would it make sense to not let hands such as the one he holds (and his draws) improve for free?

As played I think I have to call the river against his sizing. So I guess I'm fine with my call down

Well, as you see the population is raising too wide from SB so you should lean towards a 3b pre. If hes cbetting so much you could raise the flop.

So far we see that hes raising too much, cbetting too much, so his range is waaay too wide on the turn and you should definitely be betting AJ for value planning to even valuebet atleast on brick rivers.

the worst thing you can have happen OTT is that he repops you but if you dont think this is likely (you do block the nuts) it would be a good place to bet esp from IP but Xing here isnt a "mistake" i dont think, and, if you didnt block the straight an X would be more likely.
id lean more towards a 3b pf