I'd probably put him on an ace. Although it's possible that he just hit the jack and your check on the flop fooled him into thinking you don't have an ace.

You are beating A2 thru A6 (5 hands), and you are losing to A7 and A9 thru AK (6 hands). If he had a big ace then he probably would have come over the top pre-flop rather than play it out of position. So I wouldn't be too pessimistic at this point.

Pot odds are almost 2 to 1 to make the call. And the prizes generally favour 1st place, so I'd be inclined to roll the dice and make the call. If he has a bigger ace then you still have some outs to hit 2 pair or a gutshot.