AQs - IP 3et pot - no initiative

Well the charts I got from you say a Depolarized 4bet (6bb) is in place here.

I think check. Villain should have a lot of Ax lower than you or a lower pairs and a lot of straight draws. A Cbet will get a call most of the time here.

His second check on Turn looks weak to me.
I think you can make him fold a lot of pairs by betting Turn and River. And of course hands like AJ, AQ..

Any 3bet stats could be usefull, but sample is really small.
If I would 4bet I would make it around 30bb iin position.

On turn I would consider to make a small bet to try to get villain out of the hand. Villain looks like a decent player. if it was a fish I would play the hand the same what you did.

Cheers,
SDK1987

My default line would be to attack checks aggressively so i'm betting the flop for about 1/2p which does a few things you take advantage of any fold equity and take the initiative.We then have control of the pot on the turn as villain mostly checks to us and if villain raises the flop we have an easy fold.