Line check HU 200NL

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 http://www.flopturnriver.com/phpBB2/.../smiles/7c.gif, http://www.flopturnriver.com/phpBB2/.../smiles/7h.gif
Hero raises to $6, SB raises to $20, Hero calls $14

Flop: ($40) http://www.flopturnriver.com/phpBB2/.../smiles/as.gif, http://www.flopturnriver.com/phpBB2/.../smiles/jh.gif, http://www.flopturnriver.com/phpBB2/.../smiles/9s.gif (2 players)
SB checks, Hero bets $25, SB calls $25

Turn: ($90) http://www.flopturnriver.com/phpBB2/.../smiles/5s.gif (2 players)
SB checks, Hero checks

River: ($90) http://www.flopturnriver.com/phpBB2/.../smiles/jd.gif (2 players)
SB checks, Hero bets $55

i would never bet the flop unless i intended to 3barrel or at least to do so if the board got scarier.

no check, bet

actually i think that was perfect a check on the turn shos that u have sometyhing but not a whole lot then if another scare card comes u can bet especially the j because he will deffiitely think its credible that u had J something and that u hit ur 3 of a kind on the river

1) check this down
2) since you bet the flop, the turn is a very good card to double barrel. He showed weakness by c/c the flop and since usually people won't c/c fd's here you can be pretty sure he doesn't have a stack off hand.
3) River is actually a good card for his range, since there are some J's he c/c. It's also a bad card for how he probably perceives you because most people probably expect you to check a J on the flop.

agree with what max said.