The author doesn’t have to believe that industrial activity has anything to do with the weather pattern. Although the author thinks “human activity” is involved, there can be other kinds of human activity that might affect weather besides industrial activity.

Not necessary, because a premise establishes that seven-day natural cycles aren’t significant enough to cause the weather pattern. So even if seven-day natural cycles exist in the area, they’re still eliminated as potential causes of the weather pattern.

Not necessary, because if there are other locations and other weather patterns that are caused by other living organisms and not humans, that doesn’t undermine the author’s reasoning with respect to this particular weather pattern. The author can argue that this particular pattern is caused by humans without believing that all weather patterns influenced by living organisms must also involve human activity. (For example, the author doesn’t have to think that a weather pattern in the middle of the ocean must be due to human activity if it’s influenced by animals.)

Although the author does assume that the recurring 7-day weather pattern we observed in industrialized areas involves a cyclical cause, this doesn’t commit the author to believing that anything that affects large-scale weather patterns is probably cyclical. For example, an asteroid might hit the Earth and affect weather patterns; the author does not have to believe that the asteroid hit is cyclical.

Necessary, because if it were not true — if a weather pattern with a 7-day cycle (like the one we observed in industrialized areas) could have a natural cause, but that cause doesn’t have to have a seven-day cycle — then the author hasn’t eliminated all natural causes as the explanation for the weather pattern. What if, for example, a 3- or 4- day natural cycle could cause a 7-day cyclical weather pattern? If that’s the case, we can’t conclude the weather pattern we observed must be caused by humans. So the author must assume this isn’t possible.