My eyes are quite sensitive to high altitude sun, especially when I am on snow. I have suffered snow-blindness on several occasions. For this reason, I almost always carry backup sunglasses when I anticipate sustained hikes on snow.
For several years now, I have been using the throwaway sun glasses that ophthalmologists provide after an eye dilation exam as backups. They are just a thin sheet of plastic colored to block UV and bright sun and are designed to fit behind your normal glasses. They can be converted to stand-alone sunglasses with a little duct tape and a rubber band or two. I have obtained a set just by asking at my ophthalmologists reception desk; some offices may charge you for them though.
The ones that I have weigh about a gram and provide me with a bit of security and backup during my clumsy senior moments. I have, once, in the past dropped my sunglasses and watched them slide down a steep snow slope never to be seen again. Now I have an adequate backup.
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.