AK on the button - Played them too fast?

[NYCNative]

Ultimate Bet No-Limit Hold'em, $1 BB (10 handed) converter

SB ($115.60)
BB ($120.80)
UTG ($85.50)
UTG+1 ($42.60)
UTG+2 ($47.20)
MP1 ($94.85)
MP2 ($64.45)
MP3 ($64.55)
CO ($89)
Hero ($110.45)

Preflop: Hero is Button with K[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">4 folds</font>, <font color="#CC3333">MP2 raises to $2</font>, MP3 calls $2, CO calls $2, <font color="#CC3333">Hero raises to $6</font>, <font color="#666666">1 fold</font>, BB calls $5, MP2 folds, MP3 calls $4, CO folds.

Flop: ($22.50) K[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">BB bets $10</font>, <font color="#CC3333">MP3 raises to $20</font>, <font color="#CC3333">Hero raises to $40</font>...

I didn't make a massive PF reraise here like I would if I had a PP because I wasn't sure if I could get a lot of people to fold even with a $10+ reraise and the thought of making a huge reraise here and missing the flop made my head hurt.

Once I did hit on the flop, even with the raise it was only pot-sized so I wanted to make a bet that would probably make BB fold (I was thinking his small bet was a stab) and would force MP3 to either push or fold.

Thoughts?