I finished this up the other day. I have been working on using up my scraps sitting around and this idea seemed perfect for it. The materials are 1.1 oz nylon from DIYGS and 2.5oz Apex, all of which were left over from a quilt I made so I didn't spend any money on the hat (always makes me happy). It is non-stretch and I decided to not put elastic in it, but it fits on my head well anyways. The final weight of the beanie is .8oz, which beats my wool crocheted beanie by about 1.5oz.
I wish I could test it out, but it is currently 100 degrees in the Atlanta area, so it may take me a while to find a chance to actually see it in action. I did get to wear it around the house before times got too hot, and it did feel comfortable and breathed very well.
I've put a (slightly unfinished) guide to making it on my blog if anyone is interested that also has a couple more pictures.