Looks alright, can't yet fold turn or valuebet it(we can for small size but it is non-standard play and likely same deal).
I'm in thoughts what we gonna do vs 60-70% bet on the turn. Still call but not exciting spot and probably breakeven

Not sure if we can bet smallish on this flop, otherwise I was thinking about betting big anyway vs a fish profile. He might have lots of weaker aces and won't find a fold button too soon.

As played, using ~1/2psb OTF and ~1/3psb OTT, I believe his range is not too strong. And if he had something like a flush, I believe that a raise would come OTT vs your tiny bet or at least a big bet OTR when he just calls OTT.
His bet sizing OTR is not scary and he might have worse value combos and we can't assume villain is never bluffing. For a good price and taken the line the hand went, I'd be more incline to call.

But it must be checked, tho

We can't because we don't know the hole cards of the opponents... or we can just make a DB analysis and infer something?

Question: you bet 1/2 OTF, 1/3 OTT and get called, River is an offsuit 9, you check and plan to decide against a bet. Villain bets half pot, would you call? Because I cannot see many bluffs,many marginal hands improved to 2 pair and he still got the nutted hand in his range (at least, some of the times)

Flop doesn't really matter and everything from check to a bet size from 20% pot to 100% pot can work with AJ, but maybe you need more like AQ+ to bet 80%+.

Turn check is fine and I don't think I'd even fold to 70% pot OTT with AT or AJ because it beats a little too many hands that can bet turn and check down river. The GS equity also makes it less bad to call against villains set or 2pair hands. You can also bet 1/3 pot OTT and then 1/4 pot OTR against a passive player (you can vs other too but then you need to do it in a more balanced way and not have close to 100% fold vs river raises).