K-Qo questionable laydown

<font color="blue"> </font> I had just bought-in to a 10 handed, $2/$4, $200 Max buy-in, no-limit game, the game had been going for quite a while and there were 4 guys with stacks in excess of $500. The hand in question had me in middle position (3 off the button).

I hold Ks-Qc and the action went as follows (stack sizes are approximate): one limper from 3 off the big blind ($400 stack), I limp ($200 stack), next guy limps ($250 stack), button limps ($600 stack), small blind completes ($200 stack), and big blind checks ($300 stack).

Flop comes: K-8-2 all clubs

Action is check, check, check to me, I put in a pot-sized bet of $20, one fold followed by a raise to $40 from the button ($600 stack), small blind folds, big blind calls, early limper folds, action back on me. I elect to call.

Turn comes Kh so the board looks like this: Kc-8c-2c-Kh

I am first to act, I put in $60, button raises to $120, big blind folds. . . I make the laydown.

This was my first attempt at live no-limit so I was a little nervous, but I want to learn from this. I would really appreciate anybody's analysis of this hand in terms of what I should have done at each juncture in the hand; most importantly at the crucial moment when I laid it down(which, I believe was a mistake).

Thanks for any input in advance.