Go with my read or pick a better spot?

20 player NLHE home tourney with friends, $20 buyin, 3000 chips to start, WSOP blind structure, 20 minute rounds.

I made it heads up against a friend I invited, who is fairly new and was very lucky to make it that far. He hit a 4 outer and a 5 outer on the river to survive, and is calling raises liberally, especially when he's in the blinds. This was his first tournament with more than 9 players and more than a $5 buyin. A few weeks prior to the tourney, I lent him some books to read: HEFAP, SSHE, HoHE vol.1 (he didn't finish that though). He learned a few concepts, but has not had much playing experience.

When we started heads up, blinds were at 1200/600/200 ante. He had about 40,000 in chips, and I was around 20,000. I was planning to win small pots and chip away at him. However, he began to play somewhat aggressive, throwing in a pot sized bet or even a slight overbet on every flop. I was folding and I felt that enticed him to continue throwing in bets whether he had a hand or not. I was ready to take a big stand the next time I hit a decent flop. That leads to this hand:

Blinds: 1200/600/200 ante
I raise to 3000 on the button with 7-6o and he calls. I raised with the intention to steal the pot on a scary flop (which I've done a few times against him) or possibly hit a good flop and reraise when he predictably leads into me.

Flop: Qc6c3c
I hit 2nd pair, no club draw. He bets 6000. I'm 80% sure I have the best hand. However, my hand is very vulnerable and he will get a little less than 3 to 1 if I push. I feel that I'm a much better player, but I'll be shortstacked about 3:1, with less than 15 big blinds remaining.

Should I fold this and hope for a better spot?
Can I just call and push on a non threatening turn (Queen or non-club 7-2)?
Should I risk pushing this vulnerable hand even though I think it's best?

[Precept2]

You have to fold.

You have to put your opponent on a club here. That being said, you are probably ahead here, but there's no sense in pushing with second pair, weak kicker, and no club-draw. You opponent has 9 outs with 2 cards to come.

Since he's been calling liberally with any two cards, he's unbluffable. I know you're ahead, but he won't fold.

In my opinion, you'd need to dodge too many bullets this hand. Suck it up and push the remaining 15BB in a better spot.

[Benoit]

If he is as loose and crazy as you say he is, he might not even have a club. He could be pushing you off with Ace high or crap high considering you've been folding to him the whole time. You can't just keep retreating, this might be the last time you have a hand where you are ahead, and you can't bluff out the calling station.

Don't let him draw out on you for free, reraise all-in, there is already enough in the pot. He folds and you're back in the hunt, he calls and if you double up you will probably be the chip leader. If you fold this, now you will be even more desperate to double up and probably put yourself in a worse situation. And by that time you are so low in chips that a double up would barely increase your stack anyways.