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His power is illusion.The only hypothesis I have for his weapon is that he has none. He is a replicator, a being who has the ability to clone or replicate things using his own physical anatomy. If you remember what started the fight, he disguised himself as Sora, and the keyblade became his weapon as of doing so, but when the fight started he began using the Soul Eater. Also, if you look at his grave in The World That Never Was, The picture of his weapon was completely destroyed while the others were somewhat intact and able to see. As of the fact of Zexion using a lexicon that is possibly the most accurate way to explain it.