I don't have the nerve to make a hammock of Cuben nor Bill F's design sophistication, but I did find a way to cut my hammock weight in half.
I just made a 6.5 oz hammock out of some 0.6 ounce Wally World polyester lining material with Mule Tape lines. To minimize weight I made it only 9 feet long, shorter than my usual 10.5, and used 45 inch fabric instead of 60. It isn't a diagonal hammock, but lets me lie reasonably flat because the polyester does not stretch.
I have no idea whether (or when) 0.6 ounce polyester will fail catastrophically. I guess I'll find out, huh.