Sigh in the big $55

To be honest I think your biggest mistake is not folding the flop, I mean you hit the best possible card in the deck on the turn and still end up passing the river, so what really is your plan for the hand? Any spade and he basicly wins because there's no way you have a big flush draw, especially not the A flush draw, because you'd have raised the flop, even the deuce isn't a very happy card.

However given the way the hand is played I think you absolutely have to shove the turn. I completely disagree that he's not betting out with sets and even 67 because half the deck are going to be scare cards for you, and if he does have a set he's not going to be keen to give you a chance to peel off a free deuce. That said, he's also almost certainly leading with all flush draws, and pair and straight draw type hands as well as small overpairs. The J looks like a good card to him because to his mind you're more likely to have AQ or AK so he's always betting again, and there aren't very many rivers you're going to like, so you either need to pass or shove the turn, with shoving the best option.

His river bet really looks suspicious to me. He knows that you can't ever have better than 2 pair, and the 5 isn't a great card, as it's not very likely to counterfeiting 43, so a pot size bet for value is a very tricky play. The only hand I can really imagine he value bets that way is if he has 56, 57 and just wets himself and spazzes it in. It's tough, but I think given the mess you've got yourself in, you have to call the end