(Ment to post this yesterday, but comp messed up. So here it is now):
This is a simple case of not wanting to let go of a pocket pair in desperation that it might be the best hand.
You failed to display if there was straight draws, or flush draws out there. It could even be 99A, and the 99 could have helped him with 9 10 suited or something. But enough about the information you didn't give me, lets work with what you did give us.
You called the remaining 4k to leave you with 13k (I believe) with pocket jacks when you re-raised pre flop into a pot of 38.5k. Now you can have arguments that you could call for the pot odds ( 9.625:1 !!!) even though your behind because unless he has a set, you are not that big of an underdog compared to the pot odds. But then again, you do have 17k left before the call, plenty of money left with those blinds to keep playing your game and not be in all-in or fold mode.
If you thought he was on a draw, then you made the right call. But me looking onwards, I could not possibly put him on a draw. Two baby cards and an ace, what kinda draw could he have? He already stuck around 1/3 of his starting stack into the flop pre flop. And when you bet all but 4k, he's either going to go all in here, or fold and play super tight and give you a bunch of chips. He wants those chips, and he knows that it's going to give you the right pot odds to call since it's only 4k for you to call into that huge pot.
And pre flop, when you made it 6k after someone raised it to 3k, anyone would call. It's a min raise. The person who called between you and the original raiser is getting plenty of reasons to call, even with small cards and even if he thinks you have Aces, Kings, ect.
Now as for what I would have done, of course I would have called. You put yourself into a position to basically give him an extra 4k because of your bets. With someone smooth calling two times in a row is kinda fishy to me. He has got to have like a high pocket pair, or something like AK-A10 suited, or AK-AJ un-suited. He wants to see a flop before he makes a decision for the rest of his chips. There was no way to see he was going to push after you made that bet of 9k, but he did see that as an opportunity to get more chips out of you for the continuation bet. You are going to call with anything here as long as your arn't drawing completly dead.
My advice, next time, try checking once in a while in those spots. LOADS of internet and new players love to slow play hands such like Top pair strong kicker, and two pair, sets, ect. If they hit the flop, there going to slow play it most of the time. Check to see what comes out on the turn and see if he takes the opportunity to take the pot right there, or check it once more. Poker is all about a mind game, so you have to keep your opponent in check on what your going to do. Make him think your are the best player, who is unpredictable.
So all in all, it wasn't a bad move to call the all-in with jacks with an ace on board since you were getting over 9:1 on your odds, but it was bad to think he was on a draw as soon as he checked it to you. But if this play got you to the final table, then maybe your doing plenty of right moves that you just don't see. Ask someone to stand behind you, writing down some advice, good plays, good hands, ect. Then, look over it to see exactly how you are playing. Just make sure it's not one of your regular poker buddies so you don't give away free information.
