As I write this, I'm looking out my office window at a raging snowstorm. A week ago, I was reaching for the AC knob in my car on the evening commute. Holy malevolent meteorology!
Meteorology's province is the atmosphere, specifically the study and forecasting of the weather. As for the "meteor" in meteorology, Greek amateur astronomer Grigoris Maravelias explained it this way on an Internet discussion group about meteors:
Meteor and meteorology come from the root "meteor," which is an adjective in Greek. It is a compound word from "meta" and "aero." Meta means "through" or "by," and aero means "lift." So, the meaning of "meteoros" is that something happens or can be found in the air (or atmosphere).
Shakespeare made frequent poetic allusions to meteors in his plays. Back in those days, the word referred to anything that occured Up There, in the space between Earth and the celestial sphere. This included lightning, wind, hurricanes, rain, and snow, but also atmospheric apparitions that, in modern times, we associate exclusively with astronomy: comets and meteors.
Just to make things perfectly clear, when astronomers say "meteor," they mean the flash of light that occurs when a meteoroid from space falls into Earth's atmosphere and burns up. If a chunk survives and makes it to the ground, we call that a meteorite. If it's a rare type of meteorite and you are lucky enough to find it, we call that "get rich quick."
If I had to make the call, I would say that astronomers are more loved than meteorologists. When astronomers forecast a meteor — in the older sense of the word — it usually means a spectacular comet or a meteor storm. Now that astronomers have laid claim to all the fun meteors, the poor meteorologists are cursed to be bearers of bad news — like snowstorms in mid-April.