I saw this OR hat at a local shop:
http://www.outdoorresearch.com/en/or-gear/hats/sunshower-sombrero.html
It is a ventilated sun hat that includes a fitted Pertex rain cover. The cover folds up into a small envelope pouch sewn into the underside of the brim on the back/neck side.
It seems like a pretty good idea for warm weather showers, but you get a much more breathable hat for sunny conditions. I like the concept because hiking here in the Southeast in the rain with a hood is miserable. However I'm not sure if the Pertex is really any better than a cheap nonbreathable cover, a la a drill instructor in the bad old days.
The listed weight is 4oz, which isn't too bad if the performance is there.

