Preflop
Standard open, and the intention is to fold to a 3-bet, unless the 3-bettor is very short like <10BB. The main property of this hand is, that it block the reshove ranges.
Flop
This was a pretty good flop for your range, but on the other side you got called by two players, and none of them were BB. And for that reason you are not supposed to be C-betting your entire range here, and A7o has very little going for it. So I think, this is a hand, which you want to check and basically hope, button checks behind. And if he bets, probably just let him have it. BTN also needs to worry about SB, who naturally checked to you, so its not like, he can bluff himself to high heaven here.
Turn
This is the problem with C-betting to wide, when you are out of position. Now you are stuck with basically nothing, around a pot sized bet left, and no profitable plan other than to check-fold. But luckily he check back.
River
You improve to top pair, and because of the K44-6-A board you chop with any other Ax apart from AK, A6 and A4. If I calculated it correctly, you have a bit under a pot sized bet left (pot of 12,5BB, stack of 11,5BB). So the question is, how do we best get paid here? First of all there are no busted draws, so checking to him likely dont induce a lot of bluffs. But if you jam, your hand is kind of obvious, and it is at least possible, that he find a fold with hands like K9s or 77. Which should be most of his range after calling you on the flop and checking back turn.
So I do think, its sort of ok to go for a small block bet here, but because you are so short, I would probably size it down even more. When he jam, its weird, and he should not be floating you on the flop with to many A high, because he was not closing action, and stacks were so short, that he had little room to maneuver later. So I dont think, its that likely to be a chop. But you are getting better than 3:1, and it could be a chop. So even though I am not loving the spot, I cant see myself folding either.
Results
So he was slowplaying top boat, and it worked out perfectly for him, since the river card allowed you to catch up to a second best hand. Spots like these are always annoying, but I dont think, you did anything really wrong here, other than C-betting the flop.