He isn´t really going to c/f his overpairs on that turn card, so yes check behind is generally better. Also I think your sizing is a littlebit wrong. You always want to make impression that you can bluff there, so for example he´d bet/3-bet flop with A7s or 78s. So for that I´d make flop raise to 8$ that would leave him enough money behind to make bluff 3-bet or 3-bet himself for value with worse hands
Although against 70/49 you can always take line which you take and see how he shoves turn his A6