A 13/7/4 doesn't have most of the time a set here. He would have raised on flop or turn.
I think the most likely holdings are 88-JJ with one spade, or a A with a spade. A set would be possible but I don't think it's very likely here.
I prefer a check/call a bet up to $8-9 and fold higher. If villain bets 1/2 or 2/3 we are most likely beat.