I'm going to bump this one more time. Thanks for all the comments.

Seems like he either has:

a) a massive hand like top set that's looking to CRAI on the turn (I'm an 82/18 dog)
b) a better ace (I'm a 73/27 dog even w nut flush draw and my 5s as an out)
c) an overpair (QQ/KK) that now doesn't look so good (I'm an 84/16 favorite)

A check seems better against a) and b), and against c) you're probably only getting one street of value anyway. So maybe I should have checked it back.

What happened: I bet half pot on the turn, he insta-called. River was a T, he checked, I thought and thought but couldn't figure out what I was beating and checked behind. He showed QQ. I guess the question is whether he would have called another 1/2 pot bet there. I tend to think not - he has an underpair on a paired board, where it's fairly likely that I hold an A.

Given his actual hand, I would have made the most raising the flop, though I would have been taking the worst of it (I'm a 56/44 dog on the flop and he probably wouldn't fold an overpair+straight draw).

Thanks again. - Adam

I'm not convinced he's never folding AK. In fact I've never seen AK call which makes shoving better than calling IMO (because AK is like the nightmare hand for him to have if you just call - unless your planning on bluffing later in the hand).

Against AK on the turn your better to check, but its better to bet against the rest of it because he'll have an open ender/gutshot etc that'll make him want to call.

Yeah if your betting the turn you should follow up on the river. Otherwise there's only one street left and its better to minimize your losses against AK rather than make a bet on the turn and risk your stack (against that particular hand).

I would think he'd be only marginally more likely to call a turn bet as compared to a river bet (at least he should be, the value in his gutshot isn't much).

OP you said you thought that this flop hit villains hand hard (have you edited your original post?). I would argue that villain has every right to believe it has hit you harder. I would defo advocate raising it up big on the flop using your FE and getting it in.

I'd call the flop here, it is probably a 48-52, but I really do not see you having hardly any fold equity. Based on the size of the 3bet, I'm assuming villian is a complete donk and I can really only see him having QQ+, maybe AK, and he call your a flop raise with AK.

I'd check turn, you're WA/WB and if villian has QQ or KK, you're probably only getting one value bet out of him, make it on the river because in the off chance you are beat you're controlling the size of the pot.

On 2nd thought, I think the best line would be check turn, bet or make a small raise on the river. Villian is never bluff 3betting river and you may squeeze some value out of KK or QQ vs an assumed bad player/station.

? no I didn't edit my OP. All I meant was that, compared to a T84 flop it's way more likely the re-raiser has top pair/2 pair/set/OESD/straight. If it's more likely that he has a good hand on this flop, does that mean I should be playing this faster or slower?