should i have bet the turn?

Yes, you have to bet-fold turn and check-back or fold river.

Call river is a mistake: opp has 8x and 4x hands in his range, also 77 and 99.. Too many hands are better than ours.

Shurikk analysied the hand correctly....

River Donk and that > potsize => that are the nuts or even close to it very often....

I think a small bet on the turn. That way if we get raised its an easy call to try for the boat, and we wont get bluffed on the river.

I do not understand why do you miss to bet when you hit?!

Most likely scared for a straight, but betting the turn seems standard for sure and if you get raised you could consider folding here.

Cheers,
SDK1987

We cannot fold on turn as we can improve to full house...

I'd also bet/Call turn and fold to a massive donk-bet OTR

Well this spot on the Turn is a much better bet compared to a more middling board, since BB should have much fewer 4X in his preflop range.

With that said, it's fairly close between either option. Bet and call a raise if it's small enough and fold to a huge jam because you die to 89 and 4X.

As played call by default vs good players who can turn hands into bluffs (because this is the top of your range) and exploit fold vs straightforward players who only bet straights here. If your opponent is capable of floating high cards here (I guess he always calls A2 preflop + flop), this would make it a much clearer call. His pot bet makes him more polarized towards 8X and less toward 4X.