Did I bet too much?

[MilwaukeeBull]

Blinds are 500/1000, NLH. I get JJ UTG+2. I have about 8700 left and bet 4000. The button raises all in. I call feeling that I am basically committed. Button shows KK and I am done.
What should I have bet? Table was mostly on the tight side. The looser players had been eliminated, but one guy (the one who had KK) was also playing any ace.
Should I have just bumped 1000 or 2000? That would have allowed me to get away and survive had someone gone all in.
Your comments are greatly appreciated.

[La Brujita]

Generally you should bet all in or fold with less than ten times the big blind so this seems like an easy open push.

Only thing I would add is if you are close to the bubble and a decent bit of your equity came from making the money you would consider a fold. This is purely speculative based on the information your lay out and it is very very rare to fold JJ in this position.

[wayabvpar]

I am with La Brujita- if you are going to play this hand, get all your chips in early. If someone came over the top of you after betting 4k, you are pot commited anyway.

[cferejohn]

You should have gone all-in. There was no bet you could make that did not pot commit you (since any reasonable raise is more than 1/3 of your stack). You have the 4th best starting hand you can hold. If you push here and happen to run into one of the better 3, oh well, but no way you can do anything else here.