V had limped all of his hands so far. Previous hand vs me he had min bet as a bluff on a scare card.

Winning Poker Network (Yatahay) - $0.10 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

Hero (SB): 220 BB
BB: 313.1 BB (VPIP: 14.89, PFR: 6.38, 3Bet Preflop: 4.76, Hands: 48)
UTG: 100 BB (VPIP: 20.00, PFR: 20.00, 3Bet Preflop: 0.00, Hands: 5)
MP: 102 BB (VPIP: 22.64, PFR: 16.98, 3Bet Preflop: 5.00, Hands: 53)
CO: 80.8 BB (VPIP: 29.79, PFR: 27.66, 3Bet Preflop: 11.76, Hands: 48)
BTN: 95.9 BB (VPIP: 42.86, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 8)

Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K 3

fold, fold, fold, BTN calls 1 BB, Hero calls 0.5 BB, BB checks

Flop: (3 BB, 3 players) K A 3
Hero bets 1.5 BB, fold, BTN calls 1.5 BB

Turn: (6 BB, 2 players) 4
Hero bets 4.3 BB, BTN calls 4.3 BB

River: (14.6 BB, 2 players) 6
Hero bets 13.9 BB, BTN raises to 55.6 BB, fold,

2bb bet in the flop and then 5bb on the turn...on the river I’m likely gonna check to him and call of any bet given I have no read on him.

The flaw here is assuming he’s a “fish” after 8 hands. We literally know nothing about him at this point. Assuming someone is a fish based on stats or a single hand you played against them is going to get you in trouble. I’m treating V as an unknown at this point and letting them have a chance to bluff (considering you believe they have done this already) the river.

Ask yourself, what would you call 3 barrels with on this river given the way it’s played out that K3 beats?? Then ask, what do I bluff after 2 barrels and a check? A lot different ranges...

1- bet flop bigger. Bet pot or even overbet. You are not blocking top pair, neither any FD or gotter.. And your opponent is inelastic vs sizing here. So you want to put as much money in pot as possible.
2- same for turn
3- river bet is finally a good bet but 2 streets too late.. By not betting big enough on earlier streets, you limited the river bet size and messed up the pot geometry.. But bet is fine otherwise.
As played , fold this river.
Button is never bluffinf here. Like never ever! So he is value raising.
"Value" in the other hand differs in your eyes and fishes eyes!
So fish can have this range here:
AK (say half of combos, he might raise some of them along the way!) for 4 combos.
A3 (again, half combos based on above assumptions) 4 combos
43s , he might raise half of them on turn 2pair so , 1 combo
64s , 2 combos
63s , mighy not raise always so 1 combo
52s, 4 combos
K3s,K4s (above assumptions) , so 3 combos
K6s, 2 combos
A4 (above assumptions) , 4 combos
A6 , 9 combos.
If he raises this range here, which contains 33 combos , you need to be ahead of 10 of them to break even on a PS raise river

You are only ahead of 64s, 63s and 43s
Just 4 combos you are ahead, 1 you are chopping and 28 that you loose to.
So, just fold and move on...

Summary: fish has every Ax in his range and he is not raising any Ax that isn't 2 pair here. Even without these kind of analysis above, you can comfortably fold this river because of Ax in his range and him being supper passive.
Cheers

bigger flop and turn.
bet river for pure value. fold AP

seems fine to me

played fine but sizing is questionable

pot pot shove and hope he didnt hit 2pair on the turn. He is never ever folding AT/AJ/AQ and there he will call you down with any Ax at a high frequency. Because the board texture is so dry, he will have great difficulty putting you on a hand. No point in trying to squeeze out occasional 1.5bb from the reg who gonna fold OTT when you can get 95 bb from fish.