Overpair facing pair on board

[CardinalsFan]

Hello everyone! I just started playing limit holdem seriously and I am working to build up my bankroll. Anyways, this is one hand I was wondering about, because when the BB 3 bets on the flop I'm wondering if I should have folded. I'm wondering, should I call down just in case because the pot is large (20+ SB when I call)? And I think it would have been better to not bet on the turn now also. Thanks!

PokerStars 0.05/0.10 Hold'em (10 handed) converter

Preflop: Hero is MP1 with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/spade.gif[/img].
UTG calls, UTG+1 calls, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">2 folds</font>, CO calls, <font color="#666666">1 fold</font>, SB calls, BB calls, UTG calls, UTG+1 calls.

Flop: (12 SB) 7[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(6 players)</font>
SB checks, BB checks, <font color="#CC3333">UTG bets</font>, UTG+1 folds, <font color="#CC3333">Hero raises</font>, CO folds, SB calls $0.08 (All-In), <font color="#CC3333">BB 3-bets</font>, UTG calls, Hero calls.

Turn: (11.30 BB) 2[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(4 players, 1 all-in)</font>
BB checks, UTG checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">BB raises</font>, UTG folds, Hero calls.

River: (15.30 BB) 6[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players, 1 all-in)</font>
<font color="#CC3333">BB bets</font>, Hero calls.

Final Pot: 17.30 BB

Results in white below: <font color="#FFFFFF">
SB has 6c 9c (two pair, sevens and sixes).
BB has 8h 7h (three of a kind, sevens).
Hero has Kc Ks (two pair, kings and sevens).
Outcome: BB wins 17.30 BB. </font>