Weak atheism or Negative Atheism refers to the belief that because there is no evidence that god exists, we may assume that he does not exist. Weak atheists hold that there is also no evidence for existence of the god Thor, the Incredible Hulk Santa Claus or the Flying Spaghetti Monster and that as a consequence most of the earth's population do not believe in their existence.
They maintain that there is a logical difficulty in absolutely proving a negative such as "God does not exist". This is especially the case when presented with ideas such as the deist god. This supposed god does not interact with the world or humanity at all which makes his positive disproof difficult. Typically, weak atheists would simply point out that such a being is extremely improbable but accept a very small possibility that it exists. This tiny possibility would have about the same level of probability as that of faeries existing at the bottom of ones garden - not entirely impossible, but so wildly, insanely improbable that it can be safely dismissed.
Some weak atheists are not happy with the term "weak atheism" and prefer the older, synonymous, and more established term, negative atheism. This is different from Agnosticism. Agnostics also tend to say that the possible existence of God cannot be disproved, but they are less likely to say that this is a good and sufficient reason to deny his existence.