I am just begining to get into touring on bikes, but I have done a 200 mile stretch of the AT on an attempt at a thru hike. Had to go home for personal reasons but I did learn a bit about how much weight is a key ingredient on long trips. Depending on temperatures I would go with a backpacking hammack, which have a couple of key advantages.
1. Weighs 1.5 - 2 pounds
2. Comfortable now matter how rocky the ground is
3. Water dosn't pool underneath you in the rain.
4. Insect free (certain models)
5. If you have no where to hang it you can pitch it out like a tent using treking poles. Now I know on a bike tour you wouldn't have these but i'm sure you could improvise.
Henesy makes a good one called the backpackers hammock, I would check it out as an ultra light weight solution.