I think gods don't *have* to abide by the Weave. Or maybe they only have to abide by it if they happen to be on the material plane or something. But I do think they pretty much have to resort to the Weave when they channel magic to mortals. For hazy reasons. Possibly something enforced by AO, the Overgod (many rules the deities have to follow are statutes by that dude). Which is pretty much a rationale that is very... Unsatisfactory. From a narrative perspective. Basically the writers saying "because".
