Flopped set in 3bet pot - how bad is it?

[chris269]

Villain is running 31/27/6,5 over 200 hands. Normally, against a tighter player I'would have c/r or donkbet this all day. But I didn't think he was strong on the flop. The Flushdraw with overs is only a small range of all AQ/AK/KQ combinations, so I prefered value to protection. Initially I wanted to crai the turn, if he bets again. After he checked, I planned to donkbet the river, but this A was so nice, because it hits a lot in his range, plus he might bluff with any random cards. Any thoughts about it?

Poker Room skin
No Limit Holdem Ring game
Blinds: $1/$2
4 players
Converter

Stack sizes:
UTG: $244.50
Button: $209.55
Hero: $223.60
BB: $397.15

Pre-flop: (4 players) Hero is SB with 7[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/heart.gif[/img]
2 folds, <font color="#cc0000">Hero raises to $7</font>, <font color="#cc0000">BB raises to $22</font>, Hero calls.

Flop: 3[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] ($44, 2 players)
Hero checks, <font color="#cc0000">BB bets $34.5</font>, Hero calls.

Turn: T[img]/images/graemlins/diamond.gif[/img] ($113, 2 players)
Hero checks, BB checks.

River: A[img]/images/graemlins/spade.gif[/img] ($113, 2 players)
Hero checks, <font color="#cc0000">BB bets $57.5</font>, <font color="#cc0000">Hero raises all-in $165.1</font>, BB calls.

Results:
Final pot: $443.2