I'm no engineer, but I remember something my father talked about years ago. If you sandwich your entire side of 2x pieces with plywood on both surfaces (inside and outside), screwed and glued, it will form a truss and be very strong. Not sure what that will do to the weight, of course. There might be lighter materials that would work similarly.
Search a bit for foam camper builds. XPS foam is pretty rigid and some folks have built entire trailers, walls and all, out of the stuff. The Teardrops-n-TinyTravelTrailers forum has an entire thread on "foamies". Interesting reading, if nothing else, and you might get some ideas. Interior cabinets of foam would be very lightweight.
foam cabinets