Preflop
Standard open and I still like your 3BB sizing when deep.
Flop
Great flop obviously, and you can either check back or go for a small bet. I kind of lean towards checking back, because
hands like a gutshot draw or undercards to the board will likely fold even to a modest bet. The issue is, you represent this board so well, and even if you just have a hand like AK or AQ, a lot of his range has very little
equity.
So its not an easy board to get paid on, unless he specifically has AX. And as others have said, if he has AX, he is likely to lead the turn, if you check back flop, and then you can put in a raise. However you also want him to bet pure bluffs, so if he is on the passive side, just put out a small bet for value on the flop. You do bet, and thats fine, but I think, your sizing is a little to large on a board like this.
Turn
As played clearly betting again, but now your sizing is to small. You bet the same amount as you did on the flop, and we always want to size our bets relative to the pot.
River
Its weird, that he lead out on this card, because it should never help him, unless maybe he has specifically QT of spades, which made a straight. Clearly we are not folding, so its only between calling and raising, and if we raise, which size. Starting with sizing, there is so little left behind, that we should just move him all-in.
So can we raise here for value? And I think, the answer is clearly yes. Starting with the hands, that beat us, I dont think, he has AA, KK or AK, because those hands usually 3-bet preflop. He could have AJ, that he slowplayed, but there are only 2 combos of that. A2 is a loose call preflop, unless its A2s, and there is only one combo of A2s but another 5 combos of A2o, if he can have those. So at worst we lose to 8 combos and more realistically only 3 combos.
And then there are the hands, we can get value from. QT of spades is 1 combo, AQ is 8 combos, AT is 8 combos, and so on all the way down the AX ranks. People typically dont bet-fold trips on the river, when only a gutshot draw got in. So for me this is a solid raise for value, and you were just unlucky to run into the 1 available combo of A2s, which got there on the turn. In general getting stacked, when your full house runs into a better full house is not something, we should worry about. Its called a cooler for a reason.