I agree that you don't need to worry too much about what the average $5 unknown thinks about your hand range here.I don't know why you think he's so obviously full of crap though, you checked back and flatted the turn bet of his, he can easily have Ax or 6x here and figured any decent hand that you called the turn with will either make a value bet on the river or bluff (or even more simply "a lot of draws did not make it, I will check to let him bluff).So I wouldn't just assume he can't have anything here, 6x and Ax can easily get to the river this exact way and decide to check raise when the draws miss.Going back to the flop, I'm honestly a fan of just cbetting here. You take the pot down a lot when your opponent has a better weak hand (think K9, QJ, , J8 type hands that are beating you, but can't afford to call a bet).Further, even if he does flat call, there are plenty of turn and river scenarios where you can value bet your Tx, 7x, 6x cards or bluff on cards you both often miss (Jx, Qx, 9x, 8x).So I think you end up putting yourself in less ideal situations by checking back readless here. Don't forget, unless your opponent is somewhat loose, a lot of preflop calling hands will miss this flop (for pairs or legitimate draws, of course over cards happen, but are rather weak hands you can usually fold out with a street or two of aggression).

cbet flop is a must imo, we have gutshot and overs and it misses his flatting range pre quite a bit as Ryan said. As played I like the river bet but def am not 3betting river like this as imo his range is straights quite a bit.