So this an Anonymous game, with no
strong reads.I had been playing
villain HU before we got to 3handed, we played about 50 hands together and he
played very straight forward, but as I've learned the hard way in the past  with anonymous tables it doesn't mean he's not capable of taking advantage of his image.

 Didn't see too much
merit to raising turn at this point as villain should know that I know hes been playing tight
so I didn't think I would really be bluff raising this turn that often + I
wanted to have a hand that can go call/call here as I felt much of my calling
range on turn would be pair + gutter. 

The river decision is somewhat interesting once he checks. I feel I auto bet here without too much thought because we are so high up in our range in absolute strength. But the question is what kind of hands does villain have that x/c flop, lead turn, x/c river given a bet by us on the river is pretty strong. 

1) Betting this river what sizing do you use and how will you react to a x/r? I think each of these categories of bet sizes has some merritt.

      a) small bet <50% PSB

      b) medium-large bet 50-99% PSB

      c) overbet 100+% 

Also, Would you use any exploitative thinking with your bet size. Example: "If i overbet here and he shoves i can  make an exploitative fold because my range is incredibly strong and he wouldn't bluff often enough" or "If i underbet and get x/r i can call often because my hand looks like its going for too thin value" etc.

2)Checking back- given i can atleast assume villian is a compotent/agressive 10.20 reg, I wouldn't expect him to have much of a  x/c range here, he may even x/r more than x/c. Given i don't know yet how i want  to respond to a x/r, maybe Xing back is less of a mistake than betting is?