Get the thinner type of black plastic yard waste bag from a grocery store. One of those packs small and weighs about an ounce.

Not the best as a pack cover, but you can us it *inside* your pack as a pack liner.

Won't last too many days in the pack liner role; if you want something that holds up for a good long time, get a thicker "contractor" type bag of the same overall size from a hardware store. The one I use weighs nearly 3 oz, but I get a good thousand miles worth of backpacking out of one of those, perhaps more.

Even when using one of those, however, I typically carry one of the thin ones too, for exactly the sort of reason you mention --- it's handy to be able to store some things outside the tent at night. Or to sort of "stash" some things if doing a day hike but leaving some gear behind. Or base camping where you're not inclined to expose your tent to strong sunlight all day. Or you can cut one up to make a "poor man's windshirt" (really, a pullover sleeveless rain jacket) at need. Or drape over your tent at a strategic spot if you find your seam sealing job is not [any longer] completely effective --- moisture between the bag and your tent cause them to adhere well enough.

Pretty versatile item for about an ounce added weight.