Here are some good plans:
I'm guessing the design in this link could come out to less than 4 ounces if using 1.1 sil.
I've been considering giving some polycro a try for this design. I'm thinking it could be taped rather than sewn, come in very lightweight, and the seams/ folds in the corners wouldn't have to be that strong as they only have to be tight enough to lift the walls. The grossgrain/webbing tie outs could possibly be replaced with doubled or quadrupled packing or tenacious tape.
I'd like a polycro version to fit my Solomid, possibly trying to use 1/8" shock cord to lightly guy out to each corner stake (so no separate stakes are needed).