Game is 8 handed, 4/8 FL Big O.
The game has been very loose, splashy and fun. Lots of drinking and BS'ing, and lots of really big pots for this game.
Many flops are seen 6-8 handed.

In this hand, we're dealt AA457 in MP.

Calls all around in front of us, I elect to call and see a flop. Late position and SB fold so we're seeing this one 6 handed.

Flop comes: A33

So, we flop gin and it checks to me, i elect to check. I know this is meh and I could start building a pot now but I decide to just check and possibly check raise. Action checks all the way through.

Turn comes: 8

Low hits. This time the blind leads 8 and the player on my right calls. I decided to raise right here. Folds back around to original bettor who calls and exclaims - "Well, I know I've got half this pot locked up" advertising a 245 or something similar. Player on my right calls as well.

River card is 3

Wow - GROSS. So, the guy who says he has half the pot leads again. The player on my right is literally fumbling over themselves to get a raise in. This was a pretty huge tell - shaky hands, rushed breath, knocking over their chip stack. It wasn't an act at all - so there's the player with the 3.

My question is - do you call the 2-bet with the potential to face a cap or fold in this spot?

Final hand results: Player who announced he had half the pot showed up with a wonky 56 low, the player who fumble raised had the 3 and had made a full boat on the turn with the 38, they had 3568x to get 3/4.

Stopped reading after you said you checked the flop. How many people called in back of you? Your post made it seem like no one did but since you were trying to c/r I assume there were people behind you.

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Sorry if I came across as an azz but imo not betting the flop is a much more important discussion point than the once in year hands where you get one outted and squeezed

245 isnt a lock for half either.... could easily be 1/4

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Reading

Yeah that's true, a few river cards come that counterfit and he could be getting quartered already.

Given the action on the river, with a bet out and a raise, would you call 2 bets with what's essentially the 3rd nut low?

It's 6 players to the flop + dead small blind = $26 in pot on flop

no action on flop

3 players put in $16 on turn, so we're looking at $48 + 26 = $74

On river, assuming we call and our opponent who leads out flats we need to call $16 to win 1/2 of a final pot that will total $122. So we need to call $16 to potentially win $61. This is basically 1:4, so we need to be right about 20% of the time if all my math is correct.

Do you think this is worth a shrug call?

I wouldn't be that worried about making an incorrect fold on the river, given the action as described. Even bad players give us tough decisions once in a while. Not betting the flop vs this particular player also seems ill-advised.

I see no reason you can't flat the raise here in position and see what develops. If it gets 3 bet and 4 bet you can easily muck your hand, but there's no reason not to put in a call. You're obviously losing to quads, but if you know that and the blind also knows that, he'll most likely put you on a 24 as well and just call behind to avoid losing another quarter of his bet. But if the blind 3 bets there's no reason for you to commit another BB.

But I do agree with the general premise that checking the flop is a terrible idea. If it came Axx with two big cards, maybe you can allow people to catch up because there's a better chance of a scoop. But with A33, you should be looking to charge low draws full price.