Swords did not generally get heavier as armor went from mail to plate. They got more rigid to thrust into the gaps better. A Type XII cutting sword from ~1300 and a Type XVIII cut/thrust longsword from ~1500 could easily be the same weight. The blade geometry would be vastly different though.
IIRC, hardness generally ranges more across the sword than from type to type though. The portion near the grip would be softer, with the tip being harder.
IIRC, hardness generally ranges more across the sword than from type to type though. The portion near the grip would be softer, with the tip being harder.