You are both wrong. Where do you get the idea that med. European swords are overly heavy?
My second thought was William Wallace was alleged to be around 6'5" and even if you factor in some exageration due to legendary status he had to be one big MOFO for his time. If you see the sword you can tell he would have to be very big and strong to wield it.
Just guessing that the weapon had to have some serious heft- my apologies. Have read that the men who wielded these (successfully)were extraordinarily strong and agile, and had the stamina to do this throughout an entire battle. I have to admire that kind of physical ability.