4NL on Global Poker, 6-max with 5 players
I am seeking criticism on how I played this hand. The river is the part that I am unsure if I played correctly. I will post the action I made in a few hours

Hero is in the BB with AA.
UTG folds, CO makes a 2x bet to open the pot. Button calls, hero in BB raises to $0.34, CO and Button both call.

Flop ($1.04): 7 2 J rainbow
Hero bets $0.32. CO folds. Button calls.

Turn ($1.68): 5c
Hero bets $0.84. Button calls

River ($3.36): Jc
Hero checks. V shoves for $2.61. Hero?

At this point, I think it's very possible for V to have a J in his hand. The line he took could fit for a top pair or any set. Him calling a relatively large size 3bet preflop tells me he could have a range like 99-AA, probably any suited broadway or AK. With no draws on the board, it would make sense for him to call on the flop and turn when I bet into him if he has top pair. When the Jack comes on the river, should I call his shove or call and assume he doesn't have a Jack?

When you post hand histories, please include your reads on the players involved in the hand, your table image, and stack sizes because these things are very important in making decisions.

About this hand, I will assume that both villains are regs and 100bb deep.

Flop, we should bet at least 2/3 pot. But personally, since AA is very stable on this board, I will check here to protect my checking range since I won't cbet my whole range here.

Turn bet sizing is fine since we can set up a river shove.

River is a check/fold because there's no more value in shoving because we can discount QQ+ from villain's range since a reg will 3b that preflop and any pairs lower than Jx will just fold. And we can't check/call because villain are less likely to have any airs/missed draws, pairs lower than Jx will just check back river for showdown and only better hands will bet.

So hero clicks pot button, hero clicks what looks like a third of the pot button rounded to a nearest BB amount, hero clicks half pot button then hero doesn't know what to do on the river so just clicks check. Stop clicking buttons and think more about bet sizing.

Agree with the above that flop needs to be a lot more, but without knowing stack sizes and reads we can't really suggest anything sensible

Out of curiosity, what’s the reasoning behind either betting way bigger on the flop or checking to protect the checking range?

Checking back the flop to protect the checking range seems fine. To me there seems little reason to bet this flop with AA (occasionally for balance). but there's nothing to protect against.
A large bet on the flop seems weird, as you'll only get called by a jack or better (and maybe not even a weak jack) - effectively wasting you aces most of the time.

With one pair you're unlikely to get 3 streets of value. With this board texture betting turn and 1/3 pot on the river seems better to me. A shove by villain as a check-raise on your river bet is way stronger and more of an indication that you might want to release the hand (of course this depends on the villain...I know people I'd snap-call this against.)

Since hero bet flop and turn villain knows you're representing a strong hand, so he has to assume you have something you can call down with (and pay him off with...which makes a bluff less likely).

I don't understand how we're unlikely to get three streets of value with AA on a J72 rainbow board. The villain shouldn't have overpairs or two pair here very often at all. Surely they're overfolding massively if they only call down with sets.

Mainly for value. Even 1/2 pot is an improvement since we can still get all the stacks in by the river.

Because if we only check with middling pairs, weak top pairs and with give ups, then an aware reg can profitably 3 barrel us because we can't c/c 3 streets with these hands. So we want to have a hand that can c/c 3 streets when we don't cbet flop to discourage villain from 3 barreling us when we check in these situations.

Since the OP didn't have any reads on both players, we don't know if we have a fish in the pot or if both are regs.

If there's a fish in the pot, then it's an easy bet bet bet. But if both are regs and we block AJ and both can't really have overpairs, what do you think a reg will call 3 streets in 3bet pot?

Hmm, good point. With AA we block the best one-pair calling hand pretty heavily. So we'd rather have KK/QQ when we go bet-bet-bet since the villain can then have all 12 combos of AJ.

We can still get everything in by the river even if we make it 1/3 pot on the flop and 1/3 on the turn. That leaves a pot bet behind.

If we c/c 3 streets including all-in on the river, AA beats exactly a bluff. Which is the same result as we’re getting to right now.

FWIW, I am not against checking (but not checking back, we are first to act) or betting larger. Just curious why it has to be one of those two but nothing in between.

You don’t need very good hand reading skills to figure out what type of hand hero has if he 3bets pre, bets the flop into two, bets the turn and checks the river.

Yes. But I just prefer to shove less than pot on the river rather than a pot size bet shove.

We should still c/f river in this particular hand if we choose to c/c flop and turn because there's almost no busted draws that bluffs on the river and Jx just rivered a trips. But if the river is not a board pairing card, then I'll be happy to c/c a river shove.

Yup checking back flop is terrible here. We should just cbet if we're IP.

***RESULT***
V shows K6s. Was bluffing the entire time with air.

I feel like this was still a bad play on my part just based on the action... How was I to know he would bluff with a king high after 3betting the flop?

In the end, I suppose it did tell me a lot of information on this player, so I was glad it went to showdown. But normally, I think I should fold on the river in case he holds a hand like AJ, KJ, QJ, or even JTs.