Argh, I forgot to update that! Sorry sorry sorry.
I'm leaning towards it being a flat +d4. Adding a dice based on the size of the class die increases damage A LOT.
Dual wielding definitely needs to be clarified, especially who can do it and what benefit they get. I'll think on this some more, but I'm leaning towards something like this:
Anyone can attack with two weapons, as long as neither is two-handed. When you attack, you choose one or the other to be attacking with, and use tags accordingly. Dual-wield lets you attack with both, at once, so long as both are applicable. If you do attack with both, you deal +d4 damage, and use both weapons' tags.
That means your average person can carry two weapons, but its more of a fallback situation. Maybe a sword as a main weapon, and a dagger for anyone who gets in close. With dual-wield, you're more likely to carry two similar weapons and use them at once. A dagger and a sword isn't as powerful, since their ranges are different, but two swords means +d4 damage and tags from both. I think that should make your dual-wielder happy, and it seems fictionally-sound to me.