Quote from Emcee_Squared >>

Thanks for everyone responding to the second question about the rune knight and giant weapons. I've read the comments and I can see a case for it. Feel free to disagree, but here's the line of thinking. The monster has a weapon. This weapon is oversized and does an extra hit die of damage. You pick the weapon up after you slay it. The DMG tells the DM how to handle creatures (i.e. players) wielding weapons that are oversized.

The relevant section in the DMG is not a rule of combat that says 'larger weapons do x damage.' It only explains the general rules of thumb around monster creation. Now the monsters in the Monster Manual do appear to abide by these guidelines, as you see large monsters dealing an extra weapon die, huge creatures dealing two extra weapon dice, etc. And it doesn't say that bigger monsters do more damage, it says that bigger monsters have oversized weapons that do more damage. So judging from this, I'd rule that a large monster with the greataxe attack that deals 2d12 + strength slashing damage is wielding an oversized greataxe that does double the weapon dice.

"A creature has disadvantage on attack rolls with a weapon that is sized for a larger attacker. You can rule that a weapon sized for an attacker two or more sizes larger is too big for the creature to use at all." I don't know why this statement is in here if not accounting for the possibility that players might attempt to pick these weapons up off of monsters. When else would this come into play? You would have to be creating a monster that uses weapons that are too big for it, which I can't imagine is all too common.

It does seem as though larger weapons are intended to do more damage in general. Looking at Enlarge / Reduce: "The target's Weapons also grow to match its new size. While these Weapons are enlarged, the target's Attack with them deal 1d4 extra damage." There is a similar 1d4 damage penalty for the Reduce option. The spell specifically states the weapons grow larger and do more damage. 

I think I'm going to try it this way, and if it becomes unbalanced, I'll throw it out. I did think the extra 1d6 once per turn was kind of lame.

 

 I think your reading is correct. If you are large enough to wield the large weapon then you are large enough to have its extra damage and to add on to this could someon cast enlarge on a rune knight who is at extra large size in order to let them wield (and deal the damage of) huge weapons?