Once more, hand history not converted... .

BTN: 107.11 BB (VPIP: 19.23, PFR: 15.38, 3Bet Preflop: 0.00, Hands: 27)
Hero (MP): 105.83 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Ah Ac
fold, Hero raises to 3 BB, fold, BTN calls 3 BB, fold, fold

Flop : (7.5 BB, 2 players) 9c 4d 5d
Hero bets 4.15 BB, BTN calls 4.15 BB

Turn : (15.8 BB, 2 players) 2c
Hero bets 9.61 BB, BTN calls 9.61 BB

River : (35.02 BB, 2 players) 4h
Hero?

All seems standard. The question is, do we bet river or check call? Which comes down to how often does villain have a missed hand vs a made hand with which he calls. I check called but the more I look at it the more it seems I should bet myself.
Betting ourselves also allows us to bluff more with missed draws ourselves.