Weapons made of heavy metal, how would this affect damage?

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Suppose I give one of my players a (unmagical/mundane) sword or mace made of an especially dense metal, like, I dunno, uranium or plutonium or osmium (of course I'd change the name to something fantasy-like so it wouldn't be jarring), how would this affect base damage?
For example, in D&D 3.x:
A Medium steel Battleaxe for medium creatures weighs 6 lbs according to the Player's Handbook.
Making it out of uranium (almost 3x density) would make it around 18 lbs.
Would that affect damage? Or is that not enough of a weight increase to warrant such?
What about made-up metals that are extremely dense, that would make it weigh, say, 90 lbs.
Would that be enough to, say, make it count as a weapon sized for Large creatures, along with the penalty to attacks?
What about autistically heavy weapons? Like, say, pic related (in real-world myth, if I recall correctly, nothing's special about Mjolnir by itself except it weighs 2 tons), or you're fighting an avatar of the Demigod of Blades and his is somehow made of the material of the core of a dwarf star, which would weigh (if my math is right) about 255 tons. Assuming he has the Strength score of, I think, 82-85 minimum to swing that sucker around, what would happen if it happened to connect with your player's sternum?