[beachbum]

Knowing your opponent's folding equity here is huge. I think the biggest factor in this situation is your table image. Have you had similar situations previously at this table where you bet every street, he c/c'd every street, only for you to showdown an overpair or a set and he's crushed. Sometimes it only takes a couple hands like this for him to give up on the turn next time. Focus on the metagame/table image issues to figure out whether he's scared of your turn bet.

As a default against an opponent who you mentioned "doesn't like to fold postflop" I check behind this turn in this situation. No reason to get a big bet in the pot drawing thin. Take the 'free card'.