"It always amazed me how they could have wielded those huge swords."
One thing is that they're not as heavy as they look, and another is that you can use the weight of the pommel to rotate the blade when cutting, which takes a lot less power than waving the whole thing around.
Beyond that, the medieval swords were not really designed for cutting so much as puncturing. A knight's blade is no rapier, but is really shaped like a metal punch, which, of course, it is. It's purpose was to be driven straight forward, to puncture armor.
Once gunpowder made heavy armor an obsolescent nuisance, swords got lighter, longer, and more aimed at cutting or puncturing flesh.