Oh dear, did you ever. Villain seems sensible on the flop, but that doesn't mean that you can' represent AQ or KQ here and take it down. Villain's bet of 20 into 36 communicates something along the lines of "oh [censored], someone is finally playing back at me." Maybe he has 99 or A10, but he's worried. So, if you are going to check, it better be a check-raise. I would have bet out the pot here and taken it down.

By just smoothing calling the flop, you put yourself in the position where a check on the turn and a fold on the river are not horrible. You're out of position at this point and it's surely possible that villain's bet of 20 was a semi-bluff with a 9. If you were feeling adventurous and you thought that villain is capable of making the lay down, you could represent that you were chasing the straight OR that you had something very strong like QJ and was just slowplaying. You could bet out the pot, try to take it down. I don't love this line, but assuming your opponent doesn't have a 9, it's reasonable. IMO, checking is just fine here.

I think after checking the turn, a bet on the river of anything looks too weak or too strong. I don't mind your check on the river.