4NLHE set of aces vs. river shove

Hi guys, I had pocket aces today under the gun. I raised 20 cents and attracted 1 caller. The flop hit a bunch of blanks. He checked, and I knew if I bet even 10 cents he would fold because he missed the flop. The turn put two hearts on the board and he bet the pot (43 c) and I re raised to three times that. He flat called. The river hit an ace giving me a set but It also put 3 hearts out on the board. I raised a dollar and he re raised to all in. What do you all think my play should have been? Fold or call?

Why do you care if he missed the flop, besides how do you know he didn't hit a set or 2 pairs? One pair is not so strong to just give free cards. Bet between 1/3 pot and 1/2 pot.

On the river you are probably beat but it is possible that turn card gave him a weaker set. In that case he is probably not afraid you have a flush so in most cases I would call.

If I calculate correctly you have to pay 1.5$ for a chance to win 8$ (assuming 100bb stacks)... you don't have to be right too much time here.