Is this just a cooler or should I have played this slower and avoid stacking off?

PokerStars - $0.50 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: $57.41 (VPIP: 12.50, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 8)
Hero (SB): $77.07
BB: $76.69 (VPIP: 100.00, PFR: 50.00, 3Bet Preflop: 0.00, Hands: 2)
UTG: $63.78 (VPIP: 33.33, PFR: 16.67, 3Bet Preflop: 0.00, Hands: 6)
MP: $54.53 (VPIP: 36.36, PFR: 30.30, 3Bet Preflop: 0.00, Hands: 33)
CO: $63.40 (VPIP: 80.00, PFR: 60.00, 3Bet Preflop: 0.00, Hands: 5)

Hero posts SB $0.25, BB posts BB $0.50

Pre Flop: (pot: $0.75) Hero has A A

fold, fold, fold, fold, Hero raises to $1.50, BB calls $1.00

Flop: ($3.00, 2 players) 4 7 T
Hero bets $1.37, BB raises to $4.00, Hero raises to $14.00, BB calls $10.00

Turn: ($31.00, 2 players) 3
Hero bets $20.00, BB calls $20.00

River: ($71.00, 2 players) 9
Hero bets $41.57 and is all-in, BB calls $41.19 and is all-in

Hero shows A A (One Pair, Aces)
(Pre 87%, Flop 25%, Turn 18%)
BB shows 4 T (Two Pair, Tens and Fours)
(Pre 13%, Flop 75%, Turn 82%)
BB wins $151.38

You played them too fast.

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Flat the raise OTF. Villain is polarising their range here so sets/2P or air, 3Bing folds out villains weak air and gets called by better so doesn't accomplish much.

Trip barreling after 3Bing is very spewy.

What about all the Tx and flush draws that he might have played aggressively.

Villain is rarely raising Tx here, and definitely isn't calling 3 streets after getting 3B. Yeah villain will have some FDs/OESDs that we lose value from but the rest of villains range is ahead of us and it's going to be hard in later streets not knowing where we are in comparison to villains range. Also getting 4B sucks.

Don't do that

everything before river is ok even if I would not 3b AA on flop, but river shove is terrible much better is x/c.

3 betting flop is a mistake imo.

So many players lose extra money by trying to get maximum value out of premium hands. Yes, you want to get max value, but when the conditions are right for it. Too many players force the issue and end up paying off big with these hands. It is why calling 3-bets with 76s is can be pretty profitable when you're deep enough. The reverse implied odds are usually horrendous for most players that have big hands.