grunch

There is no case for either a bet or a raise on the turn. You aren't bet/raising to protect your hand, since you don't have one. You aren't bet/raising since you have large pot equity, because you don't (you're putting in 1/3 of the money, but only winning about 1/6 of the time, so you don't want to jam the pot). You have the odds to see if the SD comes off on the river: check call is the right line here.