According to what Cid an Belsar both said they've already fed at least 1 primal to each of the weapons.. from the fight with Saphire weapon..

What we know is that primals can pull us into a world during the fights.. most notablely the fight with Tsyukiomi the memories from Tsyu and the moon stage at the end..

So it stands to reason that the weapons can also harness this power from the primals being used as energy cores along with the auracite data from the Garliean commanders