What is Atheism?

Atheism can be EITHER a lack of belief in a god (weak atheism) or the position that there is no god (strong atheism). The position that that there is no god is a positive claim and carries a burden of proof. 

The lack of belief in a god is not a positive claim. The lack of belief that there is no god is a perfectly valid way to describe a weak theism. However religion DOES NOT position itself that way and neither do most theists. They make the positive claim that a god exists. Atheists simply reject that claim. 

No, a burden does not attach to the rejection of a claim. Consider a criminal trial. The positive claim by the prosecution is that the defendant committed a crime. It has the burden of proof to demonstrate that claim. The defense rejects the claim. The defense DOES NOT have to demonstrate that the defendant is innocent but simply that the prosecution has not met its burden of proof. 

Atheists find god not guilty of existing. 

This is basic epistemology 101. The person making the positive claim has the burden of proof. Those rejecting the claim need only show why the evidence is insufficient to justify belief. You can apply this to fairies, unicorns, leprechauns and big foot. I reject the claim that these things exist. By doing so I don't acquire a burden of proof to show that they don't.