Here is a good web-site on spinnaker cloth as used for spinnakers in the sailmaking industry. Spinnakers are those big colourful balloon-like sails that modern racing boats use downwind. The sails need to be strong, yet light. It is also important that they don't absorb too much water, because that makes them heavier. The ones for really light air sometimes do breath and absorb a little, so that they lift better as long as they don't get wet.
Point I am making is that spinnaker cloth varies. The first spinnakers were made of silk, soon replaced by nylon. A new material called Cuben fiber is now coming into use, and can be lighter still. In backpacking circles we call this Cuben fibre, not Spinnaker cloth, even though it is principally used for Spinnakers.
OK, here is that link..
Sailcloth weight converter,
which will explain why 0.5oz Spinnaker Cloth actually weighs 1.02 to 1.13 oz per square yard. http://www.sailcloth.com/
Click on the sailcloth weight converter!
If you think about what its designed for, it has many backpackign applications. The stuff on the upper bounds of each generic band will be more waterproof, but not the total waterproofing you may want for a tarp. If you want to waterproof it yourself you might want something on the lower end of a band as it might absorb your own waterproofing better. The stuff on the lower end also makes a nice semi-breathable wind layer. The absolute lightest nylon spinnaker cloth is about 0.8 oz per square yard, but you are more likely to find stuff that weighs 1.0 oz per square yard left untreated or 1.5 oz per square yard if its been waterproofed. If there is a sailmaker in your town I would start there. They may also make you an excellent tarp if you give them a pattern. They are also used to making stuff like sail covers, sailbags, duffel bags, so they could also make you an ultra-light backpack if you gave them a pattern.