Because it enables a specific player fantasy. It’s a genre with character customisation and “Fashion” which is really roleplaying a fantasy of a character you wish to be. If Plate armour mitigates more damage than Cloth armour, but you have loads of players whose player fantasy involves looking more like Gandalf than Havel then your game mechanics need to accomodate these differing character fantasies in some way and weight classes are the attempt to do so.
They could add an additional stamina penalty to heavier gear so there is more incentive for lighter gear. Not sure if it would be enough.
In the souls games, stamina regen rate is affected by the weight class, so there’s precedent for that.