Debate with friend about how a hand was played

[sfetaz]

A friend and myself are debating the way he played the hand below. I do not have reads available on the players. My friend feels like he played the hand perfectly to get maximum value. I feel like he should have been betting more to make people pay for their draws. He says he wants to see mathmatical proof that his method was less profitable.
Full Tilt 0.50/1 Hold'em (9 handed) Full Tilt Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Preflop: Friend is MP3 with 7 of clubs 7 of spades:.
<font color="#666666">3 folds</font>, Friend calls, CO calls, <font color="#666666">2 folds</font>, BB checks.

Flop: (3.50 SB) 4[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/spade.gif[/img], 7[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
BB checks, Friend checks, <font color="#CC3333">CO bets</font>, BB calls, Friend calls.

Turn: (3.25 BB) 3[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(4 players)</font>
BB checks, Friend checks, <font color="#CC3333">CO bets</font>, BB calls, <font color="#CC3333">Friend raises</font>, CO calls, BB calls.

River: (9.25 BB) Q[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(4 players)</font>
BB checks, <font color="#CC3333">Friend bets</font>, CO calls, <font color="#CC3333">BB raises</font>, Friend calls, CO calls.

Final Pot: 15.25 BB