Fixt. This is the kinda thing I'm talking about - not all atheists are the same kind of atheist.
The burden of proof can be on either, actually. Frankly, if you're making a point, you've got to bring the proof or you're just a jerk.
I'd love to say this is wrong, but I frankly don't know more than a couple agnostics... most of which are theists.
You're confusing your terms somewhat (I could also, perhaps, be a tad pedantic in the case that nobody else thinks the distinctions matter). The belief in a superior force is theist. An agnostic theist would believe that there is a higher power, but it is impossible to know what it is; they are not atheist. Therefore, not all weak atheists are agnostic atheists, either.