SB is a reg and UTG is unknown.

Im mostly curious what a good sizing on the river would be and if we are betcalling or betfolding. Its hard for villian to have a flush but 3way he can have 6x, 77 and 33. We are also deep so I lean toward betfolding, Another question would be the size of the flopcbet, I felt that on a board this dry there is little reason to bet big so I choose that particular sizing. My third question is if we should be 3betting bigger with those stacksizes.

I'd go a little bigger everywhere (because you're OOP).

I like bet/folding river for something around that sizing.

1/3b looks value heavy imo. You can confidently b/f like $15-$19 imo targeting JJ-99. Expect to never get bluffed, if he has a bluffcatcher he will call or fold not try to make you fold AA repping 4 combos

I pot flop and then go into x/c mode on that runout.

I think I would xr turn. I know you're supposed to focus more on straightforward value at these stakes, but turn is SUCH a good spot to trap. your hand is near invulnerable; this is a board where someone is likely to protection bet when checked to a fair amount; when you xr you look like (and can do that with) a draw of some kind - or even AK. hands like JJ are unlikely to bet/fold on the turn but there are a number of rivers that hinder your ability to get action from them - any 4 to a straight, A, K, Q, heart... even 8-T are troublesome. you also induce bets from hands which would fold to a bet, like T8, T9, KQss type stuff, but since you have aces those hands have very little equity against you anyway so checking and them checking behind is not so bad either. maybe a little fps, idk, but I think that is far better than betting yourself. specifically, BB's range is really strong and suuuuper likely to bet here (or to be drawing dead with like AK), which also causes UTG to be trapped in the middle, probably assuming you're checkfolding the vast majority of the time. yeah, I think check has gotta be best.

I'd go larger on the flop (not PSB though, maybe somewhere between 50-60% pot). 1/3 PSB makes more sense to me HU where we're going to be betting at a higher frequency; instead, we're OOP on a board that's admittedly not bad for us, but it's no Axx where maybe we can range bet 1/3 PSB and run villains over with range advantage. I think calling ranges are going to be a little more inelastic on this type of texture, so we can check more often and size up when we opt to bet.

I keep going back and forth on turn. Part of me really wants to pot because I don't believe villain should just call hands like 76s, 77-66, 33 OTF after the BB player calls, which means his range OTT is almost entirely worse pocket pairs, but then on the other hand I don't think we have enough bluffs to balance with to justify a large bet. And then the third option is that we can choose to check because there aren't many bad river cards and we probably want to defend our checking range with, well, something.

In practice I bet turn and get it in on the river and probably win, but it's one of those spots where I'm really confused what I'm doing with other parts of my range OTT.

That makes a lot of sense especially with villians beeing pretty inelastic

Id be setting up a river shove Villains range contains mostly 88-QQ. And as you see villain can make some very bad call downs with worse than those hands.

+1 what everyone else said (bigger flop and turn and prep for river jammerino).

and goodous for betting all streets tho for pure value.

bigger flop & turn + shove river

I like this

Yes check/raising turn is a good way to exploit pop. + if he checks back we can just jam river.
You can also overbet turn.