I grabbed the first paper at hand, which was 28# color printing stock left over from work. With a little lookin' I could find something thin and tough.
I thought about the Rite-in-the-Rain coated stock, but I would just buy the ready-made notebook by that time.
I really like the Moleskin notebooks for travel, but they are a little heavy for the UL world. I was thinking of 3-4 day weekend hikes for my 1oz. version.
You could have fun with it-- use colored stock, mix colored stock for a rainbow notebook, cut a peice of Tyvek shipping envelope or Polycro for a cover and so on. Extra points for using recycled stuff-- that last page with one line on it when you print a Web page, etc.