Coolskill, you have to realize that not having a belief that something exists can coincide with not having a belief that the thing doesn't exist.
I suppose the weak athiest is an agnostic who has a weak sense that God does not exist, but the sense is not strong enough, or corroborated clearly enough for them, to say they know for sure. Hence the term "weak athiest".
A similar situation to a theist who doesn't really know God exists, and doesn't have have a strong sense, but still has the idea that God probably exists.
Both of these ideologies could be called agnostic, but why not accept the gradations instead of lumping everyone together? And let agnostic be the pure idea of , "I lean neither way, I don't know at all."