What is the right spelling for weather?

"Wheather" is not an English Word. Perhaps you mean:

weather: the atmospheric conditions that comprise the state of the atmosphere in terms of temperature and wind and clouds and precipitation; "they were hoping for good weather"; "every day we have weather conditions and yesterday was no exception"; "the conditions were too rainy for playing in the snow"

whether: means "if" and is used only inside sentences: I don't know whether to bring an umbrella or not.