Was debating raising the river but I figured the only hand that calls a reraise has me beat.

PokerStars - $0.10 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

SB: 106.6 BB (VPIP: 35.29, PFR: 5.88, 3Bet Preflop: 0.00, Hands: 17)
BB: 323.4 BB (VPIP: 45.00, PFR: 22.50, 3Bet Preflop: 10.00, Hands: 42)
UTG: 67.4 BB (VPIP: 33.57, PFR: 5.59, 3Bet Preflop: 1.61, Hands: 147)
Hero (CO): 184 BB
BTN: 107.2 BB (VPIP: 50.00, PFR: 50.00, 3Bet Preflop: 50.00, Hands: 2)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K A

fold, Hero raises to 3 BB, fold, SB calls 2.5 BB, BB raises to 5 BB, Hero calls 2 BB, SB calls 2 BB

Flop: (15 BB, 3 players) Q A 7
SB checks, BB bets 7 BB, Hero calls 7 BB, fold

Turn: (29 BB, 2 players) 6
BB bets 14 BB, Hero calls 14 BB

River: (57 BB, 2 players) 2
BB bets 27 BB, Hero calls 27 BB

BB shows A T (One Pair, Aces)
(Pre 27%, Flop 12%, Turn 7%)
Hero shows K A (One Pair, Aces)
(Pre 73%, Flop 88%, Turn 93%)
Hero wins 105.4 BB

At these stakes you should have shipped the river or reraised the turn in my view.

AQ is a bit of a worry but the BB is raising real light.

Reraised turn and gii there or else ship river.

Pac... you realize how deep the stacks are when you suggest pushing as a HUGE overbet with only TP?

Are you pushing to fold out villain?

I'd push there with some bluffs, some sets and some strong top pairs. It's 5 cent/10 cent. The standard of opp dictates the play and people at these stakes have trouble throwing away top pairs.

I would always 4-bet pre vs this min-squeeze. I don't particularly want to play this hand multiway.

Since you did just call, there's no good line post-flop except for calling down. Villain's triple-barrel reps a polarized range. He's usually either very strong, with AA/QQ or AQ/A7s/A6s/A2s/AK, or he's much weaker (i.e. bluffing), and none of his weak hands should call if you raise. Your hand is just a very good bluff-catcher, not a monster you can raise for value. Use it to catch bluffs.