Villain is tight passive (I wasnt completely sure about this at this point in the match since I havent seen many showdowns but find out later on he is). Barely ever 3bets, only for value. Whats the optimal line here on all streets? I knew I was completely behind his range on the flop and only way I can win is by betting the Ace on flop. Should I have just given up after flop was called? How bad is the check on turn? What about river?

PokerStars No-Limit Hold'em, $2.00 BB (2 handed) -

SB ($256.50)
Hero (Button) ($291.50)

Preflop: Hero is Button with ,
Hero raises to $6, SB raises to $20, Hero calls $14

Flop: ($40) , , (2 players)
SB checks, Hero bets $25, SB calls $25

Turn: ($90) (2 players)
SB checks, Hero checks

River: ($90) (2 players)
SB checks, Hero bets $55