Trip aces on the flop - no idea how to proceed

[Songwind]

This was my first ever hand at Paradise Poker. I had no idea how to proceed. Is worrying about overpairs here monsters under the bed?

Paradise Poker 0.02/0.04 Hold'em (9 handed)

Preflop: Songwind is BB with 6[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/heart.gif[/img]. CO posts a blind of $0.02.
UTG calls, UTG+1 folds, MP1 calls, MP2 calls, MP3 folds, CO (poster) checks, Button calls, SB completes, Songwind checks.

Flop: (7 SB) A[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/diamond.gif[/img] <font color="blue">(7 players)</font>
SB checks, Songwind checks, <font color="CC3333">UTG bets</font>, MP1 calls, MP2 calls, CO folds, Button calls, SB calls, <font color="CC3333">Songwind raises</font>, UTG calls, MP1 calls, MP2 folds, Button calls, SB calls.

Turn: (9 BB) T[img]/images/graemlins/club.gif[/img] <font color="blue">(5 players)</font>
SB checks, Songwind checks, UTG checks, MP1 checks, Button checks.

River: (9 BB) 3[img]/images/graemlins/heart.gif[/img] <font color="blue">(5 players)</font>
SB checks, <font color="CC3333">Songwind bets</font>, UTG folds, MP1 calls, Button calls, SB folds.

Final Pot: 12 BB

Results in white below: <font color="white">
Songwind shows 6s 6h (full house, aces full of sixes).
MP1 shows Js Ks (three of a kind, aces).
Button shows Kc 4c (three of a kind, aces).
Outcome: Songwind wins 12 BB. </font>