I think he checks all the hands you beat on the river and i think he bets some of his hands that you beat but have improved like AQ and KQ. Since he check called the flop and turn i'm happy discounting 33 completely. He might bet A3 some of the time too. So the range i'd give him on the river {JTcc 45cc 89cc A3s KQ AQ}

Text results appended to pokerstove.txt

119 games 0.000 secs 23,800 games/sec

Board: 3c Kh Ac 2h Qc
Dead:

equity win tie pots won pots tied
Hand 0: 82.353% 82.35% 00.00% 98 0.00 { AKo }
Hand 1: 17.647% 17.65% 00.00% 21 0.00 { AQs, A3s, KQs, JcTc, 9c8c, 5c4c, AQo, KQo }


I'd be calling.