Hand discussion

Hi guys! I was playing micro-stakes poker, only one table with 6 players. I had AJ off suit, and I raised x4 BB in the button. Other played re-raised almost 8 BB. The flop was 8 8 J. The other player made all-in, I called but lost because he had KK. I had a slightly bigger stack than him.

Did I play well or should have fold?

It is very difficult to discover that KK maybe the preflop resubisa can make you doubt, but after the flop it seems that you have a better hand