t1riel's advice is good. Did you get to see what he had, though? Chances are - and this has no real effect on how you should have played the hand, but it might make you sleep better - that he would have folded had you bet, anyway. Maybe there just wasn't more cash to be made here.
But a re-raise on the turn is probably a good idea. At that point, he might either put you on a bluff (and possibly push all-in), have absolutely nothing and fold (in which case you haven't really lost anything), or put you on having an A kicker (but no pair) and want to see the river.
My girlfriend plays some SnGs on PokerStars
(play money) and was in the big blind with K3 yesterday. No raises, so she checked it and got to see a K-K-K flop. She had it easy, though. Seven people saw the flop, four people went all in on the flop and the turn, without her having to do any raising at all :P