I would check/call the flop, as I would check most of my bb 3bet range with a K in it and allow him to have some bluffs in his range.
You block the NFD, so when you bet (and he is tight) a lot of his range includes a K. However, your flop bet sizing and then the check make you appear weak so he could be making a play, so maybe calling with the plan to fold to a river bet as he will be checking back most of his non-K hands.