Chad:
Eagle Creek has a model that weighs in at 3.5 oz:
http://www.eaglecreek.com/accessories/travel_necessities/Nimbus-SL-Travel-Umbrella-40429/
It appears to be more or less the same thing as the Skinny Mini available at your local office superstore (the Staples down my street carries them), see:
http://tinyurl.com/jm3rw
Personally, I wouldn't trust these six-ribbed lightweights in anything but a light breeze. I have personal experience with a non-folding umbrella–not made specially for hiking, but modified as per Jardine's instructions–hiking the PCT through a rainy june in Oregon. There is no better way to stay comfortably dry than under a brolly. We hiked through a week of constant rain–and wind–and, while wet from the waist down, remained dry and warm above. A shaft bent slightly when I fell on mine slipping in the snow, but It takes a stiff wind to actually destroy one of the simpler models. Once, it was too windy, but we were on the move and found our windbreakers adequate and comfortable, sans WPB coatings.
If you get the GoLight dome (the newer models of which I believe are the same as the BirdiePal lightflex) I would feel very confident in quite stiff wind–just hold it to the windward, and you have a moving windscreen.
An umbrella isn't just good for rain. I just got back from the 50 mile BaToNa trail in my present home state of NJ, and it was hot. The ticks were out in force, which forced us to don pants. I had my umbrella up almost the whole way, blocking the sun, so I could go shirtless and hatless. I was much more comfortable, and consumed much less water, than my umbrella-less partner. An aluminized version such as the Chrome Dome excels in this application. Space blanket rubber banded to the top is the best at blocking the sun, but in my experience, is hard to keep from tearing.
This interferes with pole use, of course, but see Switchback's solution:
http://postholer.com/forum/viewtopic.php?t=284&highlight=umbrella
If it's really hot, though, using poles increases your metabolic rate, and leads to even more sweating. I learned this on my last trip.
Muskrat the Umbrella Evangelist,
Andrew Wilson