Flop: bet is fine, but check also would be nice i think. 3-street value is propably not possible anyway versus reasonable opponent and its really good to include some of your flushdraws in your checking range.

Turn, yeah you have to check somewhere and out is not pretty.

River: you can easily fold versus sizing, he can have Jx, he can have some Tx, he shouldnt play really any draws from flop by this line and also he's unlikely to bet weaker Ax that large.

Personally I like cbetting here, assuming hero has worse Axhh in range, which I imagine he does. I don't think this is a board AK checks oop very often.

I wasn't too sensitive to river sizing at first, but perhaps scream makes a good point there.

I think the preflop action is pretty important when considering river. It is a good spot for BB to squeeze, UTG folded, and most importantly the person with the weakest perceived range called (hero).

From villain's perspective, we bet flop, checked turn, and could have a lot in our range that folds to a bet on river. If I was villain I'd be stabbing the heck out of that scary river.

Another issue I have is that this is the best Ax in our range by river. Maybe that shouldn't really matter, I'm not sure. Double barrel AT and AJ I assume, AK probably not in our range.

Anyway, I think a case could be made for calling here.

I'm squeezing pre.

I'd go larger otf, and I'm personally continuuing ott though a check is whtever. Prolly doing an exploitive fold here as I doubt anyone is turning KK/QQ into a bluff,.

Fold river b/c it's too assumptive to think that hero has XC'd enough hands otf to potentially be bluffing at anywhere near a balanced frequency otr. You could find a call if you thought he had some weak Ax or QQ/KK that he played this way, but that's pretty assumptive b/c it's a pretty rare way for those hands to be played.

Villain gets to the river with so few bluffs here, basically just 67s and 78s which we can't even give him 100% of the time pre. He will have some Tx and also JJ, AJ and some AK combos. Even if we give him AQ I struggle to come up with a scenario where we have more than 30% equity (we need like 29) vs his river betting range. Like Nick said, he would have to be reopening his A3 type hands for this to be a call, so as played folding river looks good.