There's 4 weapons as, [Relic] Atma (100) and [Relic] Animus (100), Weathered [Weapon] (100), and normal named [Weapon] (110).

I'll use the Relic lance Gae Bolg for my theory on these.

So my theory is that we somehow obtain "Gae Bolg Atma", I'm thinking perhaps this is a quest to up our Zenith Weapon (My guess - the new quest "Up in Arms"). From there, it looks like there is a Zodiac Atma item obtained by defeating a certain creature ("Atma of the Goat" flavor text - "The crystallized soul of a formiddable foe felled in the East Shroud.") - my guess would be this is the new quest "Trial of the Braves". I'd then think we'd turn in the Zodiac Atma with the Gae Bolg Atma to obtain Gae Bolg Animus.

Continued...