Because I have to set the bar low with the worse case scenario
IIRC, the devs confirmed that No materia will be involved. Which might be good for the wallets but this also means that the step is almost unpredictable, almost.
My prediction is that they will add a quest to alter the weapon and that it will go two ways
Once either step is outta the way we can bring that sucker to Azys Lla and presto. A weapon with customized stats that will likely be obtained just in time for the iLevel raise.
- "At the Mercy of RNG" Path: In which it will involve grinding light until the Anima weapon radiates with the blinding intensity of a thousand white hot suns. The catch is that we can get from anywhere, even PvP and killing over-world mobs. And that the light will direct add a random stats that will add from a pool that consist of...every materia effect, even the useless ones that add to resistances. Getting the BiS weapon will require a way to see which activity yields which stat for which weapon, which will change every 2 hours. Meaning a High chance to say get Spell Speed on Verethragna from a Roulette, and its always active as long as you have the quest (quitting will reset it) which means people vying for the BiS relic might wanna try getting another Weapon to use for the activites they want to do or risk getting a subpar weapon
- "A Grind as Long as War and Peace" Path: In which we instead go for the return of Books. Or rather a long set of objectives that need to be completed before increasing a stat on the weapon. The Saving grace is that we can choose what stats to use, but each list will require 100 specific mobs, 5 specific dungeons, 2 specific 24 man raid, 5 specific FATEs (which will include new ones on 3 days timers), and 5 specific Levequests (Which will also include the Large ones...and the Crafting ones). The lists will be obtained from The House of Splendors for...2000 Esoterics/Lore (depending on patch). RNG will decide the lists objectives.
Now lets relax and know that whatever step SE will bring out, it likely won't be as bad as this (or cower in paranoia and fear that might be) :P