I don't have any numerical answers, but a few direct observations that can at least bound the problem:
I have a yard of regular spandex that i roped over a pull-up bar and hung off. It supports my entire bodyweight BUT the stretch maxes out long before completely loaded. Based on some exercise stretch bands i have, i would estimate that my spandex "rope" made from 36" width regular spandex maxes out the stretch at ~80lbs of force. For a hammock, thats probably not going to be enough, even if you doubled it up.
Notes:
Regular spandex is going to be much stronger than "stretch mesh" and other derivatives. Its also going to be much heavier. Its surprisingly sturdy stuff.
Regular non-stretch fabrics used for hammock bodies have a certain amount of inherent stretch anyway. Stretchier fabrics are not everyone's cup of tea though. Some people like the harder fabrics for support.
Stretchy hammock fabrics tend to leave you feeling... sunk down, for lack of a better term. Your heavier areas will sink in very far and your lighter areas will stay up high, giving you an awkward "caught in a net" position. My krinkle-taffeta tablecloth hammock is like this.
If you tried to incorporate stretch fabrics into a segment of a hammock body, you run into the problem of stitching. If you evenly load a line of stitches, its not a concern (many hammocks have a stitched end channel). But if your bodyweight in the hammock is mostly down the middle and you load mostly a few stitches in the middle, that could be a point of failure.
Positioning a stretchy hammock is also tricky. If you set it up to be 12" off the ground, you expect it to stay that way when you get in. If instead you sink into the ground, thats bad.
You might also look into Mayan style hammocks. They are typically made with cotton yarns but they exhibit certain stretchy dynamics you might like.
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