If you're also willing to sacrifice thickness, Dyneema/Spectra fishing line is probably about as light as you'll get. A large range of strength is available so you can match it to your application (but be sure to account for strength reduction due to knots). I certainly want my guy lines to be weaker than my tarp (but that can also be achieved with a weak link if the guy lines are too strong).
I've had good experience with
Tuf-Line which is also easy to find. It also comes with an olive green coating.
My own measurements:
130 lb coated - 0.39 g/m (0.013 oz/yd)
500 lb coated - 1.3 g/m (0.041 oz/yd)
130 lb is pretty thin; I probably wouldn't want to use anything less than 250 or 300 lb simply because it's too thin.
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