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?

Stack sizes? Anyway if u have $4 behind you at start and so does ur opponent then your committed on river imo.