I think you should make your cbet smaller since it is a 3-bet pot.
If villan is any good everything he calls us with except TT and AK is ahead of us(tying with JJ). I think TT flats on the flop and I don't think AK raises here excepting with the flush draw. It might also be something like middile pocket pair looking to hit big, and might have.
If villan is bad things still don't look that good for us. If he is bad enough to flat KQ or AQ to a 3 bet we are still solidly beat.
Frankly I don't know why you bet the flop at all since only hands that beat us call. If you check you might be able to squeeze some value from other hands.
I understand why you flatted but any hand, even a bluff, that raises us on the flop follows up on the turn I think. Rack it up to being OOP.
People love to get bluffy at this limit, but villan has shown strength, and it is up to us to get the money in good. Putting in our stacks at a thin place like this turns us from the top 30% down to the losing 70%.
I'm not very good at poker though, so take my opinion with a grain of salt.