Middle pair on Ace high flop, then nut flush draw

[c_strong]

I had only played a few hands on the table so had no reads. I'm not sure of my line on this. Obviously I'm not loving the Ace on the flop but a c-bet is standard here I think? I was planning to check or fold the turn unless my hand improved but I thought I might knock a low Ace off his hand when the third flush card hit, while having outs to the nut flush if called. I didn't put him on a flush as he called an almost pot-sized bet on the flop.

I think I should have bet more on the river. My thinking was that villain would be unlikely to call any reasonably sized bet without a spade, so I just wanted to milk a little bit more from a pair, while tempting a high spade to play back at me. Probably better to 1/2 pot it and see what happened. Comments on all streets welcome.

PokerRoom No-Limit Hold'em, $1 BB (4 handed) converter

Hero ($101.60)
Button ($62.65)
SB ($24.20)
BB ($44.90)

Preflop: Hero is UTG with K [img]/images/graemlins/spade.gif[/img], J [img]/images/graemlins/club.gif[/img] .
<font color="#CC3333">Hero raises to $4</font>, <font color="#666666">1 fold</font>, SB calls $3.50, BB calls $3.

Flop: ($8) A[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/spade.gif[/img], J[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
SB checks, BB checks, <font color="#CC3333">Hero bets $7</font>, SB folds, BB calls $7.

Turn: ($22) 5[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets $15</font>, BB calls $15.

River: ($52) 9[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets $10</font>, BB calls $10.

Final Pot: $72