flopped set - turnbet size?

[levAA]

3rd hand in the tournament 4/180

as it is a multiway pot i opend with a potsize bet on the flop, hoping for an overpair or a flush-draw to hop on.

on the turn we have a pot of nearly our remaining stacks. i thought of villain having a diamond draw with maybe 2 overcards to the board, so i assumed if he doesn't hit his flush on the turn he won't bring anymore chips into the pot.

wrong assumption?

better to make it half-size and commit him to the pot but risking to be drawn out?

what do you think makes our expectation better?

PokerStars No-Limit Hold'em Tourney, Big Blind is t20 (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

MP3 (t1480)
CO (t1480)
Button (t1470)
SB (t1420)
Hero (t1500)
UTG (t1500)
UTG+1 (t1500)
MP1 (t1650)
MP2 (t1500)

Preflop: Hero is BB with 4[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/heart.gif[/img].
<font color="#666666">3 folds</font>, MP2 calls t20, MP3 calls t20, <font color="#CC3333">CO raises to t60</font>, Button calls t60, SB calls t50, Hero calls t40, MP2 calls t40, MP3 calls t40.

Flop: (t360) 2[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(6 players)</font>
SB checks, <font color="#CC3333">Hero bets t300</font>, MP2 folds, MP3 folds, CO calls t300, Button folds, SB folds.

Turn: (t960) 6[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets t1140 (All-In)</font>