Villain is a LAG, almost a maniac, not particularly good. The match started with him sitting on about $800 stack. I struggled early on but started to adjust to him and run better, managing to build a decent stack. This is one of the pivotal hands of the match.

Poker Stars $0.25/$0.50 No Limit Hold'em - 2 players
The Official DeucesCracked.com Hand History Converter

Hero (BB): $324.20
BTN/SB: $547.30

Pre Flop: ($0.75) Hero is BB with K A
BTN/SB raises to $2, Hero raises to $6, BTN/SB calls $4

Flop: ($12.00) J A 4 (2 players)
Hero bets $6, BTN/SB calls $6

Turn: ($24.00) J (2 players)
Hero bets $15, BTN/SB raises to $35, Hero calls $20

River: ($94.00) 4 (2 players)
Hero checks, BTN/SB bets $65

Final Pot: $94.00

Hero?

I think we need some more imformation: how often have you been 3betting, how often has he called your 3bets, how often have you been cbetting and 2barrelling in 3bet pots, how has he been reacting to these bets, etc....

Without this info then I'd just say call the river.

BTW I'd probably 3bet bigger this deep.

I was 3-betting around 20% OOP, mostly 3-bet or fold, rarely called. He was calling my 3bets about 70%, 4-bet 7%., fold rest. I cbet like 80% of these and he would mostly float me on the flop and reraise on the turn with air.

Agreed, this deep raise bigger. Also, I'd bet bigger on the flop. If calls 70% of 3 bets then I'm 3 betting for value and will experiment w/ how much he is willing to call pf. If he re-raises w/ air on the turn then you are never folding this. But, does he follow thru on the river w/ air? If not, you are probably beat here. That said, knowing you are likely to get raised, I like a check/call on the turn instead.

On the river OOP, he would mostly check his one pair hands to me, including TPGK, missing a value-bet. He also almost always checked the nuts to me on the river. Large river bets were frequently bluffs.

It's really a tough spot for people to be able to tell you what to do. It all comes down to whether or not he expects you to fold here. Obviously his range is a Jack or air here and if he expects you to call here then it's a pretty easy fold.