20k starting stack, blinds 50/100
was around the 4th hand in, already felt as some of the players felt abit passive and had a few limpers in the first few hands.

7handed.

UTG folds
UTG+1 folds
MP1 limps 100
CO folds
BTN - Hero AK raises to 500
sb folds
BB calls
MP1 folds

pot(1150)

Flop K910

BB Checks,
Hero bets 650
BB calls 650

Actually considered checking the flop as i felt he would of flatted from the BB mainly with PP 99s/10s and it was first few hands and didnt feel like getting in tricky situations v a random in the first few hands. But decided to bet anyways as i wasn't sure if he would flat J10s/KJ/KQ/ etc

Pot(2450)
Turn A

BB checks
Hero bets 1100
BB raises to 3000
Hero calls 3000

Weird spot as v should know this cards hits my range more than his but was unsure whether hed raise worse 2 pairs for values or semi bluffs etc so decided to call

River 6
Pot(8450)
BB bets 6200
Hero?

Is it just a bit of a cooler if he has me beat? or should i be laying this down.
Also welcome any criticism on sizing or my thought process through the hand

Preflop is a bit on the big side but is probably fine in the first few levels of a liveament where people will flat absurdly wide.

Definitely wouldn't check back the flop, I think the range you're giving him is way too tight. Way too much value to be picked up before the board gets scarier ott to be considering checking back the flop. Also live players tend to peel a lot and are less likely to play draws aggressively, which are two good reasons to c-bet. I would make flop bet a bit bigger like 750/775.

Would also make turn bet bigger, like 1300/1350, and we're definitely not folding to this raise.

I would call river, obviously not loving it but our hand is too good to fold w/o reads imo. 87 never plays this way and his other better value (QJ/99/TT) may raise the flop. I think it's more likely he has AT/A9 here. Tough spot though, I can see myself folding in game due live players' ranges generally being really unbalanced, like some guys show up with QJ 100% of the time here.

Sick spot, seems like a classic cooler brewing. I feel like we're beat but I would just have a tough time finding a fold in-game.