Arguments for weak atheism
Strong atheism implies certainty, perhaps even beyond the scientific certainty with which we regard scientific theories such as gravity or germs. In a very real sense, every scientific "truth" is considered open to doubt when new evidence is uncovered.
Some formulations of God may be logically contradictory, but that does not mean that all possible gods are. If it were discovered that the real world is a simulation, as in the film The Matrix, then the creator of that simulation might well be considered a god. This does not answer the question of where that god or its universe came from, but it does share qualities that would make it godlike.
Arguments against weak atheism