Huh. Well, that one wouldn't have crossed my mind, since I never wear hats, and I didn't know you wore one, either.
On a related note, I used to wear my (long) hair in a somewhat tight ponytail everyday. I noticed the front of my hairline was receding and my hairdresser said it was the weight of the ponytail breaking the hair off in the front. I stopped wearing ponytails on a regular basis and sure enough, the hair returned to normal.