Try to get away from thinking you should play a certain way with certain hands and instead, assign ranges to your opponents and ask yourself how you should play against this range.
So you raise AA pre, get called by a fish and the flop comes 679d - You bet and he calls... What do you think he has? Pre he could have anything so then when he calls you post flop his range narrows considerably. He could have JT with a d, 2 pair, any one pair with ok kicker, a flopped flush\straight, a set etc. So how much of this range do you beat on the turn and what was the turn card? Any stats on villain? I assume you were out of position? Did you have the Ad?
Some fish will call with anything but most of the time, even with really bad players they have at least some standards post flop so on this board, depending on reads I would be inclined to slow down on the turn and see what he does then re-evaluate. You have to ask yourself what worse hands he can call with... if there aren't any or maybe only one or two then you're better off not betting because certainly, no better hand is going to fold.