Understanding ranges helped me a lot this hand.

I want to share my thought process AFTER I play the hand and ask if u find it BIAS because I know the result or is this good thinking. In play I didnt think that much and was trying to complete with my turn check.

So I'm going to try to detail it a little bit so I apologize if this will be too long.

I raise my AKs in range CO vs MP because it's premium hand and many times they call with worse aces or dominated suited brodways or just a pair 77-JJ (maybe also QQ). Sometimes I flat it but offsuit I'm almost always 3betting to isolate.
The big blind pays my Raise here. I can narrow his range a lot because he's calling a CO vs MP raise so I assume he is set mining with almost any pair or has suited brodways till maximal T9s. I don't think he has an ace here.

The flop is not that great for me but as I'm IP I decide to bet to make them fold Jx and other low pairs. So the BB calls and here I think he got AQ, KQ, QT, KT maybe KJs or JTs looking for his turn backdoor FD. I'm discounting QJ altough possible I think he is raising that always to get value from my AQ, AA, KK, etc.

The turn comes with the 9h a card that hits MUCH hard my opponnent range than mine. That 9 helps my range 0. So the momment the villain checks its perfect for my check back IP trying to hit my draws and I can see a free card. I thought about betting it because I had got more equity but it would have been a terrible mistake as KT got there QT, QK has now draw, etc. [I have to say this was important milestone in my play to be able to recognize this spots and check understanding how cards hit different ranges and not just bet because I had FD to the nuts trying to put more money into the pot. I know its small thing but it represent a lot for my play].

The river comes with a prefect card for me and villain makes terrible mistake overbetting here looking for value. Its soo obvious he has KQ or KJ in this spot. Maybe KT trying to trap turn but definetely he has K and his size is just so bad. I'm never calling that with worse and I think he is always calling my shove so I try to get maximum value and make it work. He has to put 1.60$ for a pot of 5.5$ and only losing to AK. I think villain could bet there 40-60% and fold to a raise but I prefer in his spot a check/raise folding to reraise maybe? How would you play hand if you were villain in this river?

PokerStars - $0.02 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 100.5 BB (VPIP: 25.00, PFR: 20.65, 3Bet Preflop: 13.16, Hands: 93)
SB: 153 BB (VPIP: 31.58, PFR: 26.32, 3Bet Preflop: 20.00, Hands: 19)
BB: 194 BB (VPIP: 25.00, PFR: 25.00, 3Bet Preflop: 0.00, Hands: 4)
UTG: 137.5 BB (VPIP: 17.65, PFR: 10.59, 3Bet Preflop: 0.00, Hands: 88)
MP: 100 BB (VPIP: 17.14, PFR: 17.14, 3Bet Preflop: 7.69, Hands: 36)
Hero (CO): 173.5 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

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

fold, MP raises to 3 BB, Hero raises to 9 BB, fold, fold, BB calls 8 BB, MP calls 6 BB

Flop: (27.5 BB, 3 players) Q♥ J♠ 4♦
BB checks, MP checks, Hero bets 17 BB, BB calls 17 BB, fold

Turn: (61.5 BB, 2 players) 9♥
BB checks, Hero checks

River: (61.5 BB, 2 players) T♦
BB bets 69.5 BB, Hero raises to 147.5 BB and is all-in, BB calls 78 BB

Thanks for reading !