The monster 15-pound blades we so often see are truly "bearing swords"...carried usually by a lord or king in parades and such ceremonial functions for looks. A true, hard-bitten warrior most often chose a plain, light, but SHARP and STRONG weapon for real fighting.
Most medieval swords rarely topped 5 pounds. Most also measured about 30 inches in the blade, with two-handers and Claymores (like Wallace's) going over 40 inches of blade.