Is there something in the story or the lore that explains why black knight weapons do extra damage to the capra demon? I know occult weapons are bossing weapons. However the black knight weapons don't seem to have an occult aux number.
There is nothing to explain exactly why this happens, only that it does.
Like all Black Knight weapons, it [Black Knight Sword] deals additional damage to demon enemies like the Taurus Demon and Capra Demon
Any attempt to explain this is merely speculation, but a suggestion might be that the Black Knight Weapons are similar to the Silver Knight Weapons, which have a Faith Stat requirement, and while the Black Knight weapons don't share this requirement, it's a possibility they still share a similar effect vs. demons.