Leading draw in unraised pot

[Roy6]

BB has a rather high VPIP, but he's not a terrible player. A bit on the passive side.
Is it worth taking the initiative on the flop?
A, K call hoping to catch a pair, 9T could have already paired, there's also a flush draw on the board.

On the turn I picked up a rather weak flush draw and the A is a good scare card, so I bet (intending to fold to a raise).

River is chip spewing? If he was suspicious on the turn, he is now convinced I don't have an ace. However, he is likely to fold his draws (JQ, straights, picked up turn flush draw).

Or am I investing too much in a tiny pot?

Party Poker 5/10 Hold'em (6 max, 6 handed) converter

Preflop: Hero is SB with 8[img]/images/graemlins/heart.gif[/img], 7[img]/images/graemlins/spade.gif[/img].
UTG calls, <font color="#666666">3 folds</font>, Hero completes, BB checks.

Flop: (3 SB) T[img]/images/graemlins/diamond.gif[/img], 5[img]/images/graemlins/heart.gif[/img], 9[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets</font>, BB calls, UTG folds.

Turn: (2.50 BB) A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, BB calls.

River: (4.50 BB) A[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>,

[billyjex]

i think your river bet wins about never (or at least not enough to make it profitable.)

if he called the turn that A on the river changed nothing. i just check/fold here.