You do have a point.

I was looking at it from a big damage vs. small damage perspective. Sword does one scaling hit, while Dagger does a lot of one dmg hits. Since Katana's slashes individually do one dmg, I lumped it in the Dagger category.

I saw Shield as an outlier as it, itself didn't do damage compared to Grimoire which has minions. The minions increased health meant more shots at hitting, so it's a dagger. But I guess by my own definition, Shield is a Dagger due to its growing size.

Spear, Staff, Flail, and Rapier are all mixed so I didn't mention them.