Bellagio $500+40 Hand

[beggars]

Interested in thoughts on a hand I played in the Bellagio $500+$40 last Sunday. I've never posted a hand before but this one has gotten mixed reactions from other players I've talked with.

This was around the 5th hand of the entire tournament. No reads on anyone other than to expect solid play at a game this size.

I'm dealt K-K in middle-late position. Folds to me. I raise to $200 (blinds at $50, $2K total to start with).

Guy to my left calls for $200. Big blind completes for another $150.

Flop is 2-4-9. Rainbow.

Big blind bets $500.
I make it $1000.
Guy to my left goes all-in for around $2000 straight ($1000 reraise).
Big blind thinks for about 30 seconds and calls.

$1000 to me. $3625 in the pot. It's all my chips basically.

How would you play it?