I recently went through this same question with a DIY underquilt I made for a bridge hammock.
Aiming for the minimum weight, I put shock cord at the corners, and nothing in a side-channel, thinking (hoping) that that would tension up the side edges of the UQ and keep them closed in on the hammock.
Nope. What seemed to be needed in the middle was some lifting, that was not being accomplished just by tensioning the corners.
That led to the logical next step, to put something lighter than shock cord through the channel I'd put along the side and that might have worked except the channel is a touch too narrow to admit whatever means I used to attach the lighter weight cord (a cotton shoe string) and the shock cord. Another concern for me on this UQ was abrasion due to that knot, the UQ and channel being made of cuben.
I probably could work something out with the cotton shoestring with shock cord corners, but the time/interest ratio thing passed the inflection point where I'm happy enough with shock cord in the channels.