So, thinking about a line from Eliza's story mode...
Humankind twists the facts of our lives into fairy tales. We grace them with power as their champions, and they call us Parasites or reduce our brethren to mere tools.
I think Alex Ahad said the Parasites and Living Weapons have "related, unrevealed origins," no? And that LW have a limited sentience, somewhat akin to a dog?
As such, I think the Living Weapons are Parasites that have had their human-connectivity parts removed, effectively lobotomizing them.
Now, thinking about Krieg... and Hungern... and Tod... Where's the Pest? We know that Krieg was handed down throughout the Renoire family for generations. And that, according to the wiki, "Some Parasites can go into 'minimal' states like a bacteria going into a cyst form, but it won’t last them forever."
I think that, way back when, there was likely some sort of "Four Horsemen Gang" that the Renoires fought on their rise to power. War/Famine/Death were captured and converted to something a little more malleable, but Pestilence got away. Pest can hide. Pest can be patient. Always there, never quite eliminated. "Like a bacteria." Corrupting the Canopy from the roots. Watching. Waiting for the right time to strike.
Now, what about Vice Versa?
Well, we know the Medicis made a LOT of enemies over the years. And we know Cerebella's the only person who's been able to properly use Vice Versa. Given this speculation on how to make Living Weapons, I think there was some goody-goody with a parasite who hated the Medicis and tried to break their operations. The Medicis won, killed the host, and attempted making the parasite a tool they could use. However, they didn't have quite the scientific resources of the Renoires, so the Medicis got something a little more finicky. A proper Mafioso would likely get choked by the hat as soon as he put it on, but if somebody with the original host's nature were to wear it... somebody pure of heart, like a certain circus acrobat... the hat might be more receptive.