top set top kicker faces action

Prima .1/.2 $20 NL.
Villain has $50, Hero has $20. It's about my third hand at this table and villain has limped all three.

Hero is MP with 33.
Villain is button. 4 limpers total.

Flop is 3 7 9 rainbow.
Villain bets .40. Hero overpots to $2. Villain calls.

Turn is 9 with two [img]/images/graemlins/spade.gif[/img]s. Villain checks, hero bets 3, villain min raises to 6, hero smooth calls 3 (after delaying until time almost expires).

Does anyone push here? I figure I've got the fourth nuts, behind 99 (unlikely), 97 and 93(unlikely), so I'm not scared of any river card. I know he has a made hand (top set top kicker) and he is drawing to four outs if I'm right. Should I have gone with my read and pushed right here, knowing he's probably coming along for the ride with the 9?

River is T non spade. Villain checks, hero pushes for 13, villain calls.

Villain shows A9o.

I know I did just fine (though comments always welcome), but I got to thinking, I would probably lose my stack with top trips top kicker also. How is villain's line?

[LondonBroil]

I would go ahead and gladly reraise all-in on the turn. You'll be showed 9x much more often than 77.

[amoeba]

theres no need to smoothcall the turn raise, 3 bet all in.

at this level, they aren't folding any 9 and they have 6 outs against you.

[FreakDaddy]

Yes, nearly 100% of the time I push that turn. A 9 is not folding and if someone outflopped you here, then you're losing your stack. That's poker.