The lightest case is no case. I carry no case for my glasses --- wear them during the day, set them beside me at night. When I want to use reading glasses or just see things closer without the glasses, it works fine for me to temporarily hook them into my shirt with the earpiece.

Sunglasses for me are clip-ons that are made for (and sold along with) my particular model of glasses, which I buy online at quite a bit less than from a local shop. These clip-ons I carry without a case in my breast pocket; haven't had any problem with this in limited testing (just finished doing so on a five-day backpacking trip along the coast).

If in pretty bright conditions, I'll fashion home-made side shields to keep out glare.

The one case I do carry is for my reading glasses, but I use a pretty small, light pair of these; the reading glasses themselves weigh 12g (0.4 oz), the case 15g (0.5 oz). I've tried lighter alternatives, but find that I just don't want to use anything that I've found that's lighter.