I think once he checks there's a good chance he's beating you. Even if he isn't, he could make some weird play with AK or bluff you somehow and you end up getting in a spot like you did where its unclear whether you should call or not. Checking also controls the pot size.

Then again, this is 5nl and you may find that players will call it off here with tons worse. If that;s true than you should be betting the flop. The above analysis is assuming that if he has AK, AQ or a pair worse than yours he's calling 2 streets maximum.