Playing draw

I was playing limit draw on poker stars.

I raised, got one caller behind me, drew 2. He drew 2.

I didn't bet after the draw, he called, I showed JJJxx, he showed AAKxx

I guess he kept a King kicker to his pair of aces.

What did he think I had? If I didn't have trips my most likely hand was something like 77A. It was very unlikely I'd have drawn two to something link AAJ.

Why did he keep a kicker?

Correction: I did bet after the draw.