Up until the river is pretty standard I think. At river I wasn't sure whether I should just bet half pot and fold, or if I should check with 2nd pair and call a bet that isn't too large. I think the problem with 1/3 pot is that my hand gets quite face up, though that probably isnt a problem against a fish. When he floated me 2 streets and goes all in on the 3rd heart I expect him to have made a flush an overwhelming amount of the time and it is easy fold.

PokerStars - $0.05 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 69.4 BB
SB: 92.8 BB
BB: 100 BB (VPIP: 32.00, PFR: 22.97, 3Bet Preflop: 0.00, Hands: 76)
Hero (UTG): 211.8 BB
MP: 138.2 BB (VPIP: 23.17, PFR: 17.98, 3Bet Preflop: 6.80, Hands: 776)
CO: 121 BB (VPIP: 41.43, PFR: 37.86, 3Bet Preflop: 21.05, Hands: 144)

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has J A

Hero raises to 3 BB, fold, fold, BTN calls 3 BB, fold, fold

Flop: (7.4 BB, 2 players) 5 9 J
Hero bets 4.8 BB, BTN calls 4.8 BB

Turn: (17 BB, 2 players) 6
Hero bets 13.4 BB, BTN calls 13.4 BB

River: (43.8 BB, 2 players) K
Hero bets 14 BB, BTN raises to 48.2 BB and is all-in, fold,

I would check the river here and probably fold to most bets.