You're confusing terms here, and your premises are false.
Strong atheism says "I have evidence to believe that there is no god, therefore there is no god"
Weak atheism says "There is no evidence that god exists, therefore I will behave as if there is no god"
The first is a deductive argument, the second is an inductive argument, you take the premise from an inductive argument, mash it up with the conclusion from a deductive argument, and of course you are able to rip it to shreds (Because inductive arguments cannot make statements of certainty in the way that deductive arguments can.) This is a classic case of the straw-man fallacy.