How much did I need to reraise the villain?

[lijkie]

Here is the situation: Its Pokerstars 180 ppl 20$ NL tournament. The blinds are 100$-200$ and im sitting next to a very aggressive player with 10.000$, known to play any two cards.

My stack size is 4.000$ and im dealt KK.

Villain raises double the big blind to 400$. I am next to act and raise to 800$. All fold to villain, who calls. I really wanted him to call so I raised him only the minimum.

Flop comes JT6 rainbow. Villain bets 600$. I raise to 1200. Villain reraises and I call allin. Villain shows 66 and wins the pot.

Did I raise to little? What did I need to raise preflop than? Or was I going to loose anyways?

Some advise please!