If you think about it, any nylon or plastic good enough to offer your tent meaningful abrasion and puncture protection is going to be pretty hefty in weight.
For me, with or without groundsheet, it just pays to spend 2 extra minutes to inspect the ground -- the area is small -- so kicking off sharp objects really is pretty easy. So, if you are going to do the inspection anyway, you don't need to haul hefty protection. In any case, most all nylon/plastic provide very poor protection against puncture from sharp objects anyway.
I didn't read all the replies so apologies if this is a repeat. I've been using 2-mil plastic sheeting (aka painters cloth) that's available in any and all hardware stores, Wal Mart, etc. One roll costs $2-3 and provides enough for 2-3 groundsheets. I'm on my third one in 5 years of use, averaging 10 bag nights per year. Weight for one cut to the size of my Seedhouse 2 SL is just under 4 oz.
The plastic sheeting will help keep your tent floor clean and dry -- and provide some abrasion resistance. My Seedhouse is 4 years old now and the floor is still in perfect condition.
What with condensation and all, the sheeting is sometimes wet with mud in the morning. It's a lot easier shaking/drying the sheeting and then folding the dirty side to itself -- then trying to pack a tent with a wet, muddy floor that you know will make the entire tent -- inner and outer -- all wet and muddy.
Tyvek will work too, but I dislike them. Tyvek is a bit heavier, but a lot more bulky compared to 2-mil plastic sheeting. Tyvek also has a habit of attracting dirt to its surface (static?).