AKo, 2nd nut flush draw, raise out 3rd or keep in?

[CanKid]

BB is fairly loose passive, but reasonable. UTG I have no notes/hands on.

If I'm raising the flop to knock out the 3rd, explain why it's better than keeping him in, hopefully tying him if a H comes and he's mid-low heart, which he'd likely fold for 2 on flop.

Party Poker 5/10 Hold'em (6 max, 6 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Preflop: Hero is Button with A/images/graemlins/club.gif, K/images/graemlins/heart.gif.
UTG calls, <font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">1 fold</font>, BB calls, UTG calls.

Flop: (6.40 SB) T/images/graemlins/heart.gif, 3/images/graemlins/heart.gif, 7/images/graemlins/heart.gif <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">UTG bets</font>, Hero calls, BB folds.

Turn: (4.20 BB) T/images/graemlins/diamond.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">UTG bets</font>, Hero calls.

River: (6.20 BB) 6/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">UTG bets</font>, Hero calls.

Final Pot: 8.20 BB

What do you think the BB will fold that would clean up equity for you? K7, A3, and possibly K10. And I don't think you will buy yourself a free card very often as your hand is pretty transparent so call.