From memory of the few fabric-covered airplanes I've been around, the doping process actually makes the fabric quite stiff, more like a thin sheet of plastic than the conventional notion of cloth. I suppose it's really more of a composite, similar to fiberglass cloth with a resin binder.
Should give pretty light construction, though, since even with all the wing area, the covering for a Piper Cub weighs ~40 lbs out of IIRC about 800 total.
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