$5 NLHE 6-max: 300BB hand. What to do this river with the nuts???

Only 4 hands on him.
Fold to cbet flop - 1/1
Barrel turn - 1/1

pokerstars - $0.05 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

BTN: 289.2 BB (VPIP: 75.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 4)
SB: 23.4 BB (VPIP: 20.83, PFR: 16.67, 3Bet Preflop: 0.00, Hands: 27)
BB: 101.4 BB (VPIP: 33.33, PFR: 11.11, 3Bet Preflop: 0.00, Hands: 67)
UTG: 157 BB (VPIP: 24.44, PFR: 17.78, 3Bet Preflop: 0.00, Hands: 48)
Hero (MP): 261.2 BB
CO: 101.4 BB (VPIP: 16.28, PFR: 9.30, 3Bet Preflop: 0.00, Hands: 133)

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has Ks As
fold, Hero raises to 3 BB, fold, BTN calls 3 BB, fold, fold

Flop : (7.4 BB, 2 players) Qd 2s 8s
Hero bets 4 BB, BTN raises to 8 BB, Hero calls 4 BB

Turn : (23.4 BB, 2 players) Td
Hero checks, BTN bets 11.2 BB, Hero calls 11.2 BB

River : (45.8 BB, 2 players) Js
Hero checks, BTN bets 22 BB, Hero raises to 80 BB, BTN calls 58 BB

How am I gonna play this river?? Should I have just lead & gone for value? Or check raise & try to scoop the whole thing?? Or is my sizing good enough to get a call balancing his range???

I honestly don't know if I like the check... on the river. He has a lot of hands that will gladly check behind when the straight and the flush show up on the river. Calling a raise Preflop on the button, he could have a pretty wide range, but raising your CBet narrows it down a little bit. AQ KQ QJ QT, or any medium PP like 99,88,77. It's unlikely he's got AA or KK, and he didn't 3 bet your preflop raise... because you block those, but it's not out of the question, and it's also possible he has a set.

The hands he's going to call a big check raise are AK, QQ, 88, and QJ or QT. I think he will check behind with all of the rest of his range rather than getting a huge reraise behind a value bet. Then again... I am out of practice, so my thoughts are probably wrong.

Don't like the check either.

Glad it worked out though...he's probably a fish. Generally, if a flush hits or board pairs on the river, players are going to shut down and try for a showdown (unless they have it). In this hand, a profitable bet from you is around 1/3 pot on the river. Half pot would probably work for you here, and that's the route I would usually go.

Jamming 300BB would be very polarizing and quite scary for him.

You don't have enough info on him to know whether he'd fold the 2nd nuts. But you did end up winning about 1 normal stack