x/back flop

Pre: Perfect, 4betting here is definitely an option but my preference is definitely to call the three bet.

Flop: I would lean towards a check back here. We have 10 outs to improve on the turn and AK high is going to be good here sometimes as well. We will almost never be folding out a pair here so the types of hands we do fold out are normally going to dominated by us so I think betting here was a substantial mistake. As played then when we get raised it's a fold.

Turn: As played we are definitely folding now, if we had checked back flop though villain would likely be betting somewhere in the region of 60c which we would be able to call and see a river.

You have showdown value, backdoors, you can't possibly fold out overpairs and you can't bet for value. For me, it's a pretty easy check back.

As played you can't really continue on the turn.

Even over a small sample, villain's 3bet stat should be pretty worrying. 2.3% is 1/43 and that's hard to do if villain has a wide 3betting range. It's not impossible, but it's hard to do.

For that reason I don't expect many hands worse than AK. Fast forwarding to the flop that means you're still not doing very well. Combined with a very suspicious check on an obvious cbetting board I would go with a check back.

I much prefer a check back on the flop. Even though villain has checked his range is still super tight and I would expect a check raise here more often than usual.

As played the turn is an easy fold for a bet that size.