Why meteorology the study of weather and weatherology is not?

Answer 1

Most studies (-ologies) get there names from Greek roots. Weather is not a Greek word. The "meteor" in meteorology essentially refers to "things high up" i.e. the sky.

Answer 2

Meteorology is the study of the atmosphere and its characteristics, while weatherology isn't a recognized scientific term. Meteorology focuses on understanding and predicting weather patterns and phenomena, whereas weatherology is more of a colloquial or non-standard term that may not have a specific scientific meaning.