I use Sketchup a lot, mostly for architectural applications, but I have used it to design a few large, inflatable sculptures that were sewn. In a few weeks I want to start designing a tarp tent, and I'll probably use SU. I use SU 8 Pro, with a bunch of plugins.
If it were me, I'd model my design in SU, copy the model, then select and make a group or component from each face in the copy (which would correspond to individual pieces of fabric). Separate the pieces, rotate so they are all in the same plane (there may be a ruby script to do this, but I don't have it) then use the offset tool to add basic seam allowance for sewing. Tweak as necessary, for flat-fell seams, etc. Draw a big rectangle corresponding to fabric size, make it a group/component, then arrange pieces on it for most efficient fit. Export as .dwg or .pdf (reguires SU Pro). Tweak as required. Prototype in cheap materials.
Apologies if this is essentially what you already do. I suspect any program that will automate the fiddly steps above will also be big $$. SU will certainly let you calculate surface area (thus weight) and rough volume. Obviously, SU models rigid planes that don't behave quite like fabric. When I've used it to model fabric forms, I rely on experience with sewing to get close, and then prototype.
The plugin "Soap Skin Bubble" might help visualize how flat shapes in fabric will bulge and curve. The book "SketchUp for Site Design" by Daniel Tal has a lot of good stuff on modeling, including canopy forms. I like both sMustard and Sketchucation as sources for plugins. I've just started playing with SketchyPhysics, which might have applications
Recent versions of AutoCAD incorporate 3D design. I have the latest AutoCAD for Mac, but really don't use it enough to say if it would work for you.