Here a collector weighs some of his historic (or replicated) swords and other weapons on camera.
Results are roughly:
Heaviest 2handed sword: 7 lbs
bigger swords, usable 1 or 2handed ("bastard sword"): 3 lbs
various 1-handed sword types (including rapier): 2-3 lbs
battle axe, warhammer: under 2lbs, lighter than most swords
smallsword (a gentleman's dueling weapon): less than 1 lb
spear: 3 lbs
2-handed axe: 4 lbs
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