The other player called an initial raise and then your raise, it is safe to say this player has either a decent pair, a good ace(AK-AQ), or is a donk. If the caller had KK or AA they would have pushed back at you after the inital bet and your raise, they did not which puts us back to decent pair or good Ace (or donk, which means good luck no matter what).
With the above information, the continuation bet could have been avoided and the hand declared a loss with an A on the flop. Players love aces, and I hate to see them on board when I have KK-QQ-JJ. While this was by definition a continuation bet, it really was not. The stakes were too high for information gathering, you either were going to take the hand down right there or face an all-in shove re-raise. If you are planning on using a continuation bet with JJ if A, K, or Q on board when in reality it is an all-in situation for the other player, then you are better shoving all your chips pre-flop once the first raise hit the table and the villian called.
Bye
