cant we just check behind and show down the winner?

Do you really expect to be often ahead vs a hand he c/c'd twice with?

his stats seem reasonable and he has called a 3bet oop so he has .... double suited connected, single suited rundowns, double pairs ? We beat all the rundowns containing 9!Q, many of which pick up GS's on the turn, we beat KK+pair..... Dont we bet the turn expecting to be ahead of villain's range? what has changed on the river?

lol, just occurred to me how dumb that question is, he has called again, that's what has changed. still think we win reasonable amount though

You beat all one paired hands, alike KK JJ… and what 2p+ you think you can fold out on that board thats not scary at all - its highly unlikely you have 45 , so , if you pot it, what you expect to fold out ?

I think he calls all better folds all worse, probably doesn't fold 2p with this runout. I wouldn't. He is nitty so most combos of 63 have either 57 for a double ender 45 for a straight or 55/44 that also raise with fold equity. He could also raise a lot of 96 combos on the turn so only thing you are beat by is Q9 and i don't think you are folding that. If he x/c 96 on turn cause he is afraid of the straight and wants to keep pot small, Q is a blank so i dont see him folding that either.

I felt like his range was somewhat capped and mostly consisting of random low 2pairs he might fold to a 3ball cause I should be able to convincingly rep Q9 or some random set. I also don't think he perceives my bluffing range as that wide because most of my hands should have some SDvalue and take the free SD in his eyes.

It's true that I win vs some hands but I don't think that's the point at all. I don't expect him to c/r bluff with those ever so the result vs them is the same, no matter if I bet or check back.

It's just a question of how many of his 9x and lower 2pairs I can get to fold and shouldn't he rather raise the turn with those a lot? Would you slowplay 54 in his shoes on the turn?

Let's call the number of hands in his range A, and the number you lose to A'

So on the river, if you check behind you win 23.05 * (A - A')/A = 23.05 - 23.05 * A'/A

Now, if you bet .... say 15 on the river. Lets call the number of hands that he calls with B (all of which beat you), and we'll assume like you said that he is never bluff raising, for simplicity.

you win 23.05 * (A - B)/A - 15 * B/A = 23.05 - 38.05 * B/A

So, what has to be true for the bet to be better than a check?

23.05 - 23.05 * A'/A < 23.05 - 38.05 * B/A

38.05 * B < 23.05 * A'

B/A' < 0.61

Remember B is number of calls, and A' is hands that beat you, two pair or better. So for a 15 dollar bet to be better than a check he has to fold more than 61% of his two pairs+.

A) Your range contains so many other hands that want to bluff that considering bluffing with AA here is comical. 

B) He's never folding 2pr.  He's not calling with enough KK/Qx.

C) You do have some showdown value.  You beat stuff like 987*,KK,JJ+gutter, etc etc. 

Take a showdown here and bluff with hands that have better removal effects or that are more towards the bottom of your range.