Still early, but this is 3rd time guy has CC my PF raise in position. Both hands before played out in a similar way, me raising broadway cards, then c-betting with air on the high, low, low boards.

I always seem to dust off chips early in these spots, where I lead both flop and turn, then check/call the river a marginally better hand.

Full Tilt Poker No-Limit Hold'em Tourney, Big Blind is t40 (9 handed) Hand History converter Courtesy of PokerZion.com

saw flop|saw showdown

Hero (t2740)
CO (t2955)
Button (t5765)
SB (t2580)
BB (t3480)
UTG (t2715)
UTG+1 (t3775)
MP1 (t3225)
MP2 (t2720)

Preflop: Hero is MP3 with , .
4 folds, Hero raises to t120, 1 fold, Button calls t120, SB calls t100, BB calls t80.

Flop: (t480) , , (4 players)
SB checks, BB checks, Hero bets t360, Button calls t360, SB folds, BB folds.

Turn: (t1200) (2 players)
Hero checks, Button bets t1080, Hero folds.

Final Pot: t2280

Results in white below:
No showdown. Button wins t2280.

Well your check on the turn certainly leaves it wide open for him to take it from you. Maybe throw out a smallish bet but nothing wrong with the line you took. I may check flop and see what villain does.