flop a set, river brings semi-scare card

[Maulik]

this hand had me thinking. its a huge pot to pick up the first hand of a tournament. people constantly call to the river w/ hands like Q10, QJ in the $10s.
So I check behind, because I'm out of the tournament if he's called me to the river w/ his backdoor draw. If he was hoping on taking all my chips w/ the 'good river' then I'm still in positoin to play for 1st w/ t500, not really a terrible thing.
Discuss?
Usually I'll bet there, but this was the first time I can recall HU that I checked behind given the circumstances. It is possible I lost way too much EV by not betting half of the pot there, too.

NL Texas Hold'em $10 Buy-in + $1 Entry Fee Trny:14606175 Level:1 Blinds(10/15) - Saturday, August 06, 19:12:12 EDT 2005
Table Table 35259 (Real Money)
Seat 3 is the button
Total number of players : 10
Seat 8: gn1331 ( $800 )
Seat 1: Hero ( $800 )
Seat 2: Dishwasher1 ( $800 )
Seat 10: mspe1960 ( $800 )
Seat 9: hedgeyurbets ( $800 )
Seat 6: pocket_apes ( $800 )
Seat 4: layak1 ( $800 )
Seat 7: dopey_daddy ( $800 )
Seat 5: oldawg ( $800 )
Seat 3: JohnnyMahoz ( $800 )
Trny:14606175 Level:1
Blinds(10/15)
** Dealing down cards **
Dealt to Hero [ 3d 3s ]
pocket_apes folds.
dopey_daddy folds.
gn1331 folds.
>You have options at Table 11588 Table!.
hedgeyurbets folds.
mspe1960 folds.
CokeFiending calls [15].
Dishwasher1 calls [15].
JohnnyMahoz calls [15].
layak1 calls [5].
oldawg checks.
** Dealing Flop ** [ Kh, 3c, 9c ]
layak1 checks.
oldawg checks.
Hero bets [50].
Dishwasher1 calls [50].
JohnnyMahoz folds.
layak1 calls [50].
oldawg folds.
** Dealing Turn ** [ 7h ]
layak1 checks.
Hero bets [175].
Dishwasher1 folds.
layak1 calls [175].
** Dealing River ** [ Td ]
layak1 checks.
>You have options at Table 11588 Table!.
Hero checks.
layak1 shows [ 5s, Ks ] a pair of kings.
CokeFiending shows [ 3d, 3s ] three of a kind, threes.