Honestly, I doubt that a Strength 20 D&D barbarian cares about the wrong weight of his Greataxe, given that they can probably deadlift a horse. Their player probably does care that the chosen implement of murderous doom looks cooler than a plain Daneaxe…

One problem that D&D and videogames have, is that weight in lbs is a pretty poor simulation of the burden involved. The sheer bulk or lack of proper carrying opportunities seems factored in a bit into several RPGs, even those where you can carry 111 spears in your backpack.

The (vastly underrated) tabletop RPG RuneQuest once ditched "lbs" and went with a more abstracted "encumbrance" (ENC) statistic. And of course lots of videogames plus several tabletop games go with a slot- or grid-based inventory as a main or secondary source of being overburdened.

Weapon weights and similar issues (too short rapiers, non-existant back scabbards) seem to be the "not every weapon is a AR-15/mind your trigger discipline" of the HEMA crowd.