A tripod's stability relates to its construction principles and torsional rigidity more than weight.
Perhaps stability is being used to mean different things here. Stability meaning resistance to being pushed over, as by a wind,
is related to weight and to the geometry. Torsional rigidity has nothing to do with stability meaning resistance to being pushed over, within the range of forces a photographer is likely to encounter.
Torsional rigidity and vibration damping also relate to weight, because both depend on the elastic modulus of the material and the mass of material. For practical purposes, any desired level of rigidity can be achieved with any material if you use enough of it. Where design comes in is (1) the diameter of the legs, assuming they are hollow, because larger diameter means more rigidity for the same weight, and (2) in the joints between leg sections, because the joints are always much weaker in bending than in compression, so their ability to support a weight along the axis of the legs is excellent, their ability to resist a force applied to one side may be poor.