I played this like a chicken.

Villain was SB. He had not been out of line.
25NL. Both I and villain had full stacks ($25+).

I had AA in middle position and raised $1 (4x). Villain called

Flop T98, all spades, I had the Ace of spades. Villain check-raised me $1.5 to $4.5 (6x to 18x). I called.

Turn Kd. Villain bet $5 (20x), I called.

River 6c. Villain bet another $5, I called, he showed JJ (no spades).

Even though I won the hand, I thought I played it very weakly, if not horribly. Could I have played it differently? e.g. Would it have been a push or fold situation on the flop?

I'd have prolly pushed the flop.