Ummm... I haven't played poker in a while and I wanted to hear some thoughts.
Live 5-10 at the Rio, 7 handed, HJ is youngish British person who seems fairly competent. We have no river history yet. We both have 1k. I'm
Folds to Villain who raises to 35, I call on the BTN with A

2

, blinds fold.
1. (Do people like calling here OTB with this? 78s? 8Ts? ATs? I feel like all hands aren't great to flat here with even IP. If we do flat, we can't be playing fit or fold right? Is there any basis behind this reasoning besides general intuition?)
Flop: K

6

3

Villain bets 50, I call.
2. I like floating here better than raising. The board is static. Thoughts?
Turn: 9

3. Villain checks. I decide to 2 barrel here because Villain seems to have a capped range here and I think he might c/c, c/f a lot of his range. Sizing? If I don't think villain has a high river folding %, I shouldn't bet at all correct?
River: J

4. Villain checks. I??? Bet? Check? Sizing? What is villains river range here? I'm thinking it often could be KxQ

or
My main question here is preflop. BTN calling range and why? Math support?