$25 NLHE 6-max: sick river spot

PokerStars - $0.25 NL (6 max) - Holdem - 4 players
Hand converted by PokerTracker 4

BTN: 196.84 BB (VPIP: 23.79, PFR: 16.73, 3Bet Preflop: 4.35, hands: 278)
SB: 100.56 BB (VPIP: 21.87, PFR: 18.50, 3Bet Preflop: 10.05, Hands: 550)
BB: 101.88 BB (VPIP: 34.62, PFR: 30.77, 3Bet Preflop: 0.00, Hands: 27)
Hero (CO): 112.48 BB

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has A:diamond: K:heart:

Hero raises to 3 BB, BTN calls 3 BB, fold, BB calls 2 BB

Flop: (9.4 BB, 3 players) 6:spade: 6:diamond: K:diamond:
BB checks, Hero bets 6.72 BB, fold, BB calls 6.72 BB

Turn: (22.84 BB, 2 players) 2:heart:
BB checks, Hero bets 15 BB, BB calls 15 BB

River: (52.84 BB, 2 players) J:club:
BB checks, Hero bets 30.28 BB, BB raises to 77.16 BB and is all-in,???

Don't think he is turning missed flush draws into bluffs here. 6x seems to be in his ~34% vpip range and KJ definitely is.

My question is, could we have bet smaller on the river, maybe 1/3 pot? We still get value from worst Kx hands and maybe get a crying call from Jxd and some 77-TT that floated 2 streets. A lot easier to get away from the jam. The only thing is that you have to balance some nut hands with this type of bet on the river not to get exploited with a bunch of river jams over 1/3 pot river bets.