[10NL] KJo, SB vs BB, facing big river bet.

Villain is 44/27 with 4% 3bet over 110 hands. Seen villain 3bet a premium (AKo) and have seen villain defend his BB fairly wide (53s, 76o)

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

Hero (SB): $10.83
BB: $13.24
CO: $12.94
BTN: $10.15

Hero posts SB $0.05, BB posts BB $0.10

Pre Flop: (pot: $0.15) Hero has J:spade: K:diamond:

fold, fold, Hero raises to $0.30, BB calls $0.20

Flop: ($0.60, 2 players) 5:spade: 2:heart: K:heart:
Hero bets $0.40, BB calls $0.40

Turn: ($1.40, 2 players) 4:club:
Hero bets $1.00, BB calls $1.00

River: ($3.40, 2 players) 6:spade:
Hero checks, BB bets $2.80, Hero ???

Again, hand seems fairly standard up until the river. I have my own thoughts but I want to see what other people think first then I'll explain my actions and thought process.

Big bet from villain on river...Hero?

I think I prefer a turn chk/call as most regs float too wide in this spot on the flop and bluff the turn. Plus we won't get two calls from the weaker one pairs in his range and there's not much chance of being outdrawn on the river. If he has Kx we'll get one more street from him no matter what.

River is sticky but I just don't see what we beat when we look like Kx and villain can't expect to bluff us off it. Villain won't be betting one pair Kx hands either and probably checks back the flush draws that turned or rivered a pair.

What's villain's AF?

This is a close spot. He sounds like the type of villain that will have a lot of 3x here. Is he the type that will bluff a bricked FD?

I lean towards folding given sizing, but I think it's close for sure.

I think I'm calling this. He's very likely got hearts, the question is if he has the 3h. I feel like if he has he bets less because he won't want a king to fold. This looks oversized and I suspect it's a bluff.