I don't have a zip model, but I have noticed the undercover does become load bearing for me. This may be due to your weight, I'm within 12-15% of the max of my hammock and the undercover was just too tight for my personal taste (and seeing as how it belonged to a friend, I didn't want to damage it), so I made my own.
What I discovered in that process was that the UC was being stretched too tight length-wise. I would offer that you start by trying to decrease any excess room on the suspension line between the mitten hook and the end of the hammock wrapping. (IOW, pull the mitten hooks as close to the center of the hammock as possible)
That will cause the UC to sag more, reducing the opportunity for it to be load bearing. Another thing I would offer is to increase the length of shock cord on the bottom opening. The design (flaw?) of the shock cord on the opening causes it to remove any excess material along the length of the hammock body, which can also lead to it being load bearing if the material doesn't end up laying properly. Tying an extra 6-12 inches of shock cord to the line already tied in will help this not pull as much.
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