KK late $10 180...as chip leader facing loose big stack push on flop

[ssnyc]

I'm the chip leader by a pretty nice margin with 40 or so remaining in PS $10 180 pp tourney (pays 18)...Villan seems pretty loose (few hands ago he played 2 4 suited from EMP in a raised pot and got it all in on flop with middle pair and flush draw (he beat 99 by catching flush on turn)

How is my play here? Is 4X too little pre with position vs a loose player? Do I instacall the push here?

PokerStars Game #10729851400: Tournament #54364342, $10+$1 Hold'em No
Limit - Level VIII (200/400) - 2007/07/02 - 12:50:28 (ET)
Table '54364342 20' 9-max Seat #3 is the button
Seat 1: --- (3185 in chips)
Seat 2: --- (8403 in chips)
Seat 3: Hero (24272 in chips)
Seat 5: --- (4425 in chips)
Seat 6: --- (7847 in chips)
Seat 7: villan (17512 in chips)
Seat 8: --- (8204 in chips)
Seat 9: --- (7555 in chips)

All post $25 ante
---: posts small blind 200
---: posts big blind 400

*** HOLE CARDS ***
Dealt to hero on button [Kh Kd]
villan: calls 400
4 folds
hero: raises 1200 to 1600
2 folds
villan: calls 1200


POT: $4,025

*** FLOP *** [9c 9s 6c]
villan: checks
hero: bets 4800
villan: raises 11087 to 15887 and is all-in
hero: ?? 11087 more to call