It's a little known fact that Vikings were actually extremely short: most were under 4' tall. Erik the Red is actually an abbreviation of Erik the Reduced Stature. So there you have it, modern-day fantasy dwarves are just a representation of Vikings, in much the same way that garden gnomes are another celebration of those feisty axe-wielding chappies.
That's bull. Eiríkur Torvaldsson (Eirīkr Tōrvaldsson if we use old Norse rather than the Icelandic language) or Eiríkur (hinn) Rauei (Erik (the) Red) was named "(The) Red" because he was ginger, that is he had red hair.
Dwarfs exists in old folklore from the Nordic countries but not because the people were so short, yes they were short but the folklore around dwarfs isn't there because of that, especially if you consider said stories were written by them but not by people from other countries. And the "Red" part most certainly has nothing to do with being short. The only way for Red to be anything even closely related to just being a short for "Reduced" would be if he was first named in English and then his name got translated to the Nordic languages, which it was not.
As for more info on Dwarfs I'm gonna go take a quick look into the Snorra Edda to refresh my memory about how they are explained in there.