For a ground cloth it's tough to beat plastic. A sheet of plastic 2 mil thick is very lightweight. You could carry a small roll of the stuff in your BOB and use it for multiple purposes. 4 mil plastic is very durable but much heavier. Another possibility is a sheet of Tyvek building wrap.

In addition to making an excellent ground cloth, a plastic sheet and some cord can be rigged in an unlimited number of configurations. In fact, the designer of your GoLite Cave, Ray Jardine, used plastic sheeting to make tarps long before he began using nylon.

I've used 2 mil plastic sheeting for a ground cloth on multi-week backpacking trips and it lasts just fine. Just remember to keep it from protruding outside of the tarp's footprint or it will make a great rain collector/bathtub.