Set versus possible flush

[PygmyHero]

$1-$2 Limit HE (10 handed)

I have been running good and have shown down my big hands. The table is now tightening and I feel that my winning table image will allow me to make some steals.

Preflop: Hero is in LP with 6 [img]/images/graemlins/club.gif[/img]6 [img]/images/graemlins/spade.gif[/img]
Everyone folds to the Hero in LP, <font color="red"> Hero raises, </font> CO calls, button folds, SB folds, BB folds.

Flop: (2.75 BB) K [img]/images/graemlins/heart.gif[/img], 6 [img]/images/graemlins/diamond.gif[/img], Q [img]/images/graemlins/heart.gif[/img]
<font color="red"> Hero bets, </font> CO calls.

Turn: (3.75 BB) 8 [img]/images/graemlins/heart.gif[/img]
<font color="red"> Hero bets, </font> CO calls.

River: (5.75 BB) 3 [img]/images/graemlins/spade.gif[/img]

What is the appropriate action? This set versus semi-scary to scary board is a situation I run into with some regularity. I have not been raised when the flush card hits but because I did not fill up (or make quads), I do not want to give him the chance to raise the river if he's sitting on the flush.

I am fine with any other discussion of the hand EXCEPT PF - I feel the semi-steal was at my discretion. I would love to hear some discussion of the comparative merits of going for a CR on the flop or turn.

Results in white below:
<font color="white"> Hero checks, CO checks. Hero shows a set of sixes, CO shows 77 for a pair of sevens. Hero wins. </font>