if you check to him, and he bets the turn, then he has the better hand and you'd only be calling with a draw; hence i don't get check-calling. you can c/r but that's a lot of chips to commit to what you pretty much know is a semi-bluff (maybe it's just me but i really don't see a tight player calling the flop bet from the preflop raiser then betting the turn with anything less than AK).
I think betting like you did likely folds anything but a flush or a set (which you said he didn't have), and you have outs against the set. keeping it simple and betting here is a better option here than any of the fancy options that have been suggested