Here's one way to protect two eggs with only paper (ordinary copy paper) and masking tape:
Roll a piece of paper into a cylinder deep enough to fit the two eggs, one on top of the other. Make a bottom for it & attach with masking tape. Crumple up some pieces of paper for cushioning, so you pack the cylinder with a wad first, then an egg, then a wad, then an egg, then a wad. A single strip of masking tape across the top will keep everything in (we were supposed to keep the weight to a minimum). Then roll up little sheets of paper to tape to the sides of the cylinder, so that you have "bumpers" to cushion the eggs if the wind should slam them into the wall of the building on the way down.
The REAL trick, though, is to take two sheets of paper and tape them together, flat. Then attach them with 3-4 masking tape "cords" to the top of the cylinder. Voila! A parachute!
I believe our device weighed in at about 35-40 grams (without the eggs).