For a while I used cheap, UV-blocking rollup sunglasses as my only set. They worked, and I'm sure they weighed less than their case, which was like a film canister. I wish I'd slipped some kind of smooth paper around it before storage, though, as they got scratched after a while.

They can fly off your face in a gust of wind. Running a web search, I've found that some come with a string.

No idea how much they weigh as I haven't had a set in decades.