A weather God also frequently known as a storm god, is a deity in mythology associated with weather phenomena such as thunder, lighting, rain, wind, storms and hurricanes. . Should they only be in charge of one feature of a storm, they will be called a (insert weather attribute here) god/goddess, such as a rain god or a lightning/thunder god.
In the Indo-European, Near Eastern, and Mesopotamian traditions, the storm thunder god is frequently made into the head of the pantheon after eclipsing the sky god, the original king of the gods, in popularity. If the chief god has a name unrelated to the "Dyeus" etymon, he's an example of the thunder god replacing the sky god as the head of the pantheon.
The sky god, meanwhile, has more than likely faded from the memory of the tribe and has functionally ceased to exist. In an interesting twist, the Sky Father and thunder god appear to have been merged into a single deity in the Greek and Roman pantheons, thus while Jupiter and Zeus continue *Dyeus, they wield the thunder/lightning bolt and are associated with oak trees and eagles. Storm gods are most often conceived of as wielding thunder and/or lightning (some lightning gods' names actually mean "thunder” but since you cannot have thunder without lightning, they presumably wielded both).