Bryan, I'll heartily second polycro! I bought a 2-pack from Gossamer Gear, the medium 40'x96' size, each sheet weighing a mere 1.6 oz, about eight years ago, and I'm still on the first sheet. True, it has a couple of small punctures, but nothing to render it useless. The trick is to clear the area well of pine cones and sticks, which you'd want to do anyway if you were using a tent with a floor. Tyvec sort of works, but keep in mind that it is a breathable material, so some moisture (vapor) in the ground will pass through.
A good bivy choice can be had from Equinox: ~7 oz, $60. This one works quite well in a shelter situation, be it a tarp or a dome. Happy Trails!