"one who observes the weather," 1869, from weather (n.) + man (n.). Weather-prophet is from 1784 as "barometer;" 1827 as "person who predicts the weather."
Clerk of the Weather, I deplore
That all thy greatness is no more,
As should a gentle bard;
That Nature, or that Nature's law
When you politely called for thaw,
Gave frost was rather hard.
[from "Consolatory Address to Mr. Murphy, the Weather Prophet," Colburn's New Monthly Magazine, 1838]