No Reads or Anything, overall I am pretty sure I played this hand horrid.

Poker Stars, $0.10/$0.25 NL Hold'em Cash Game, 6 Players
LeggoPoker.com - Hand History Converter

BB: $21.50
UTG: $12.50
MP: $27.75
CO: $25
Hero (BTN): $27.20
SB: $33.10

Pre-Flop: A A dealt to Hero (BTN)
UTG raises to $1, MP folds, CO raises to $3.50, Hero calls $3.50, SB folds, BB calls $3.25, UTG folds

I always see short stacks playing tight or willing to gamble with any Ace. Since a short stack raised UTG, I wanted to confuse the player by just calling the 3bet and have him shove.

Flop: ($11.60) 7 A 2 (3 Players)
BB checks, CO checks, Hero checks

Flop was so dry, so i just checked behind

Turn: ($11.60) T (3 Players)
BB checks, CO checks, Hero bets $6, BB folds, CO calls $6

Turn probably should have been a little bit bigger.

River: ($23.60) 6 (2 Players)
CO checks, Hero ?

As played, what should my vbet be? From how it was played, I figured that Villain would have a hand from 1010-KK

Its fine to call pf with aces since you are on the btn. Its good to mix up your play sometimes.

As far as taking him to value town, our river bet you can bet half pot, or just shove to try to make yourself look weak. Either is fine vs an unknown imo.

To be honest, you played this hand horribly. Raise to ~$8.00 PF. This will make it much easier to play post flop.
Checking behind on that flop (as played) is also bad, because they will assume that you will try a continuation bet here often if checked to, and you want to be getting all your money in by the river.
Your opponents are usually drawing to two dead outs, so it's better to try and make them think you're bluffing the flop.
Also, I'd bet almost full pot on the turn, but as played make it about $19 on the river

Bet more on the turn. Your betsizing doesn't really matter that much since draws are such a small part of his range. Unfortunately it looks like he has JJ-KK, so maybe bet like 15 and hope he can find a hero call.

There are places for cold calling with aces, though i tend to avoid it. Easier just to play straight forward.

But cold calling a 3bet shows extreme strength anyway so you may as well raise. You seem to want to get the UTG stack, but you may be missing out on the CO's stack which is much bigger by playing it this way.
If he had QQ,KK or something you may have got all in preflop, but now he has a chance to get away from the hand.
As played shove river, CO only has 15.5 left, so if he is going to call $10 he will call it all anyway.

The only time i flat call preflop aces pf 6handed is when i'm on the BTN, a loose guy has opened and blinds like to squeeze.

As for the hand, AA is a hand that likes a single opponent, so you have to cold 4bet here. I'd make it like 8$.

I like the way you played the hand postflop though, now shove the river.

I wouldn't make a habit of slowplaying AA at these stakes, simply because you're missing so much value by not raising and reraising with the hand preflop. Mixing up your game isn't really an issue at 25nl because people aren't paying that much attention.

I'll make an exception if there's a very aggressive player on table, who'll fire 3 barrels on the board unimproved. Flatting his raise preflop and letting them fire-fire-fire into your aces can be pretty profitable.

If I put him on JJ-KK, would villain actually call a shove on the river? Wouldn't it be better to just bet small enough to get a call?

Villain has like 15$ left. If he is calling 12(half pot) he is also calling 15.

Also, you look like you don't have an ace since you checked the flop 3ways, therefore a crying call is more likely,

calling preflop with Aces is fine if you never 4-bet. if you don't 4bet a lot and suddenly 4-bet your range is highly skewed towards aces/complete air. A lot of regulars will probably recognize this if you dont happen to 4-bet alot. Since i 4bet a lot including TT+ and random air im going to be paid off when i 4bet a greater proportion of the time since my range is wider than yours. A competent villain will be able to easily figure out that you're ahead of his range and will fold if you 4bet aces. If you start 4betting, be sure to include a bigger range than just AA.

However against most non thinking villains and against people who are just unknowns its perfectly fine to 4bet. flatting with AA pre flop is fine, and its certainly deceptive. Both have their advantages disadvantages. You will probably increase variance with aces when you elect to call preflop instead of 4betting since it will be harder to put villain on a range.

Fwiw, I flat aces usually aggainst constant threebettors and when there are loose players to act still behind me that will probably call a threebet but fold to a fourbet. It just helps build a big pot and disguises my hand.

I would bet 8-9 on the turn and shove the river.

Yeah I don't do this unless I have a specific read. AA is just too valuable a hand.

problem with calling a 3bet cold like that is you look quite strong to anybody who is observant at all. the only good reason to do this imo is if you think that somebody in the blinds is aggro enough to squeeze, and this is nl25, so that's not really going to be an issue. i dont hate your play but i think in this spot it's much better to just 4bet pre and get it in vs KK or JJ or w/e. as played i think your turn bet is fine cuz the villain can't have much on this board, and i'd vbet like $11 or so on the river

Bet more on the turn and shove the river and you would have played the hand perfect.

PF is fine. You're not worried about raising here to make it easier to play your hand. When you call here, it's going to be a 3 bet pot and you have aces -- you shouldn't have any difficulty knowing what to do in this situation. Cold calling a 3 bet does look strong, but cold 4 betting looks even stronger. Cold 4 betting just folds out a ton of UTG's and CO's range (unless CO isn't one to 3 bet light) while getting value from a small portion of their ranges. Cold calling makes UTG more inclined to stack off than a cold 4 bet, and can potentially get CO to stack off lighter too.

On the flop, I like your check. There is no reason to bet here. You have the deck crushed, and the pot is already bloated enough that you will only need 2 bets to get stacks in. Checking lets them catch up/bluff the turn.

You can bet more on the turn because anything villains calls a $6 bet with, he's just as likely to call a $9 or $10 bet with, and this bet size makes it easier for them to stack off on the river if they call. In this situation villains care more about the number of bets than the size of your bet.

River is an easy shove.