Unfortunately had no history with the opponent... We are on the bubble. I was feeling like he had AJ, AQ, AK in his range here. Not really sure if this should be a call.
Any feedback appreciated!

Winning Poker Network (Yatahay) - 750/1,500 NL - Holdem - 9 players
Hand converted by PokerTracker 4

BTN: 34.49 BB (VPIP: 24.69, PFR: 17.28, 3Bet Preflop: 9.09, Hands: 83)
SB: 36.61 BB (VPIP: 33.33, PFR: 16.67, 3Bet Preflop: 0.00, Hands: 6)
BB: 16.48 BB (VPIP: 21.52, PFR: 12.82, 3Bet Preflop: 4.00, Hands: 159)
UTG: 59.56 BB (VPIP: 21.67, PFR: 6.67, 3Bet Preflop: 3.33, Hands: 61)
UTG+1: 46.81 BB (VPIP: 9.09, PFR: 6.06, 3Bet Preflop: 5.26, Hands: 33)
MP: 8.96 BB (VPIP: 16.95, PFR: 14.04, 3Bet Preflop: 0.00, Hands: 59)
MP+1: 41.35 BB (VPIP: 19.35, PFR: 8.33, 3Bet Preflop: 7.41, Hands: 62)
MP+2: 24.33 BB (VPIP: 29.41, PFR: 25.00, 3Bet Preflop: 0.00, Hands: 17)
Hero (CO): 28.51 BB

9 players post ante of 0.1 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 2.4 BB) Hero has K A

UTG calls 1 BB, fold, fold, fold, fold, Hero raises to 3.73 BB, fold, SB calls 3.23 BB, fold, UTG calls 2.73 BB

Flop: (13.1 BB, 3 players) J A 3
SB checks, UTG checks, Hero checks

Turn: (13.1 BB, 3 players) 4
SB bets 6.55 BB, fold, Hero calls 6.55 BB

River: (26.2 BB, 2 players) 4
SB bets 14 BB, Hero calls 14 BB

SB shows J J (Full House, Jacks full of Fours)
(Pre 54%, Flop 97%, Turn 100%)
Hero shows K A (Two Pair, Aces and Fours)
(Pre 46%, Flop 3%, Turn 0%)
SB wins 54.2 BB

Why aren't you betting the flop?

Think we're missing value from hands we beat by not betting the flop.

You have under repped your hand so you kinda have to call tbh. If i was vil i would not expect to see AK here.

Yep, bet flop for sure. And then turn. But yes, the outcome wouldve been the same.

+1

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so if you're not going to cbet the flop you have to be comfortable in exactly this kind of situation or have a read on your opponent that he is aggro ott or otr vs non c-bets. with your shallow-ish stack size I'd advocate a more aggro line however, UTG is going to have a lot of ropey broadway hands that you're giving a free pull at a gutshot or a free pull at a 5 out 2 pair/trips draw. SB's range has to be a lot of PPs and some weaker Ax holdings. so vs those ranges giving free cards seems suicide

As above, in reality it's just a cooler. Sorry you lost.