Hi. I'm surprised that nobody has answered this yet. I was going to yesterday when I first read it, but waited because I figured that one of the experts would respond.
Styrofoam (with upper-case 'S') is a brand name for a particular type of polystyrene. In general, it has a low density (weight is a function of gravity), but there are different forms of it. The same stuff that makes semi-rigid insulation panels also makes disposable coffee cups and 'peanuts' for packing fragile equipment... and none of those have the same consistency.
The load-bearing capacity comes more from the engineering specifics of the structure than from the material itself. You could easily make a pyramid out of used cups that would support a person, or use beams made of the denser insulation material to build a truss system to support the same load with less volume of plastic.
A lot of things from aeroplanes to movie models are made from a polystyrene core covered with something like Fiberglas (also a brand name) or carbon fibre. It gives a very light-weight structure without compromising strength.
That's the best that I can do for you; it's not an area that I have much knowledge about.