River Checking(Stars 2-4)

Here lately I've noticed myself checking the river against busted flush draws headsup especially when I have marginal holdings. Is this play standard or should I have bet the river for value? I didn't have any stats on him, but this is Stars... Anyway I figured if he had 1/2 a brain he wouldn't continue his draw at a flush that obviously couldn't win. Therefore I put him on queens or waiting to go crazy on the river with quads.

PokerStars 2/4 Hold'em (8 handed) FTR converter on zerodivide.cx

Preflop: Hero is MP2 with 4[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/club.gif[/img].
<font color="#666666">2 folds</font>, MP1 calls, Hero calls, <font color="#666666">3 folds</font>, BB checks.

Flop: (3.50 SB) 8[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, MP1 checks, <font color="#CC3333">Hero bets</font>, BB calls, MP1 folds.

Turn: (2.75 BB) 8[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, BB calls.

River: (4.75 BB) 5[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, Hero checks.

Final Pot: 4.75 BB

Results in white below: <font color="#FFFFFF">
BB has Ts 7s (three of a kind, eights).
Hero has 4s 4c (full house, eights full of fours).
Outcome: Hero wins 4.75 BB. </font>