25 NL: Interesting spot with a set deepstacked

[Warteen]

As usual, I am posting this hand from memory, so forgive me if it's a little rough.
Villain is a regular who is a fairly solid TAGish player. I haven't noticed any big leaks in his game that have been noteworthy.

25 NL on World Poker Exchange and we are both two stacks deep. Six handed.

Hero (Button) is dealt [3 [img]/images/graemlins/club.gif[/img] 3 [img]/images/graemlins/heart.gif[/img]].
3 fold, Hero raises to $1, SB folds, Villain (BB) calls.

Flop (~$2): [3 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/heart.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img]]
Villain checks, Hero bets $1.50, Villain (hesitates and) calls.

Turn (~$5): [4 [img]/images/graemlins/spade.gif[/img]]
Villain checks, Hero bets $4, Villain raises to $12, Hero calls.

River (~$29): [J [img]/images/graemlins/club.gif[/img]]
Villain checks, Hero...

Thoughts? I believe this villain isn't playing 56 OOP for a raise, but it's possible. Just calling his checkraise on the turn was because I thought there was a chance he had A5 for the straight (and I hoped the board would pair on the river). If he has the nuts (or near it), though, why not bet the bricked river? What's the villain's range here? Are we betting our set on the river when we each still have over $30 behind, or are we sacrificing some value by checking to see a showdown since we believe our set may be vulnerable? What's my line?