This is a WA/WB situation, except, like Chuck said, we're vulnerable to overcards.
Thus, since we're taking a risk seeing the turn & river (since an A, K, or Q could come) we need to be compensated for that risk. So we'd like money to be put in the pot on each street.
My standard line here would be check/call the flop, and bet the turn. If I check the turn, and he checks behind he's got 2.25:1 pot odds
on his 3:1 draw. Combine that with the times we'll get bluffed off the pot when an overcard comes that he doesn't hit, and any bets we may call on the river when he catches up, and I'm not sure that's enough compensation for risking my hand.
Thus, I'd bet/fold the turn, and then try to see a cheap showdown on the river.