The author concludes that human activity causes the weather pattern. She doesn't specify industrial activity. Human activity includes commuting, heating and cooling buildings, gathering for entertainment, and countless other things that vary between weekdays and weekends. The author doesn't need to assume that industrial activity in particular is the driver. Even if industrial output stayed constant seven days a week, the argument could still work if some other form of human activity varied by day of the week.

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.

Without this assumption, the author's process of elimination breaks down. She eliminates natural seven-day cycles. But if a natural cause with a different length cycle (say, a 3-day or 4-day cycle) could produce a weather pattern that repeats every seven days, then eliminating seven-day natural cycles doesn't eliminate all natural causes. There could be natural, non-seven-day phenomenon generating the pattern, and the author would have no response to it.

The negation test confirms this. Negate (E): "A weather pattern with a natural cause has a seven-day cycle, but that cause does not have a seven-day cycle." In other words, it's possible for a non-seven-day natural cause to produce a seven-day weather pattern. If that's possible, then we can't conclude the observed 7-day pattern must be caused by humans just because natural 7-day cycles are too weak. Some other natural cycle might be responsible. Since negating (E) weakens the argument, the author must assume (E).