I made a case out of evazote foam, the same stuff as foam sleeping mats. From memory the base is 6mm thick about 15mm bigger than the Kindle all round with square corners, then a rim of 10mm foam, a Kindle shaped ring, then a top of 3mm foam and a stiff 1mm plastic sheet from a stationary folder. the plastic is stitched to the top 3mm. All 3 layers of foam are impact adhesived together. The top has a trap door in it big enough to reach all front buttons and see the screen. The plastic sheet has a hinge to allow the trapdoor to open. There are some recessed velcro patches to hold the trapdoor shut and an extra elastic band. The side buttons can be pressed through the foam or the foam can be stretched to get a finger inside. The Kindle comes out easily by stretching a particular rounded trap door corner open to slip it in and out. We keep a plastic bag inside to waterproof the Kindle if needed. The whole thing looks like a foam book as the sheet and base are bigger than the rest. As the foam is black white black it alternatively looks like a large liquorice allsort. It also looks home made so is less likely to be nicked.
The case weighs 28 grams. I made it as I had the foam to hand in 3 hours. I felt the screen was the most vulnerable which is why I added the stiff top sheet