So far, the best strength to weight ratio I've managed to find is stuff called 'jet line'. It's apparently used for pulling wire through conduits, but the stuff I have is basically a scaled down version of 550 cord. It's a tightly woven kern, with a stranded mantle in the center. It's very small diameter, light, and stupid strong. Most of it has a breaking strength greater than 200lbs. It's also very cheap.
An example of heavy duty jet line.
Heavier than most other jetline I've seen, 500lbs.