I had a dyslexic moment and could not remember which weather I wanted. So I looked it up. Following the advice to “blog your homework”. Here’s the answer for next time I forget.
TL;DR: Whether or not the weather is good will decide if we go to see the wether.
Wether
Wether is a castrated goat or ram. It can also be part of a British place name. You probably don’t want this one.
Here’s a Wikipedia link if you want to know more.
Weather
Weather is the stuff that is falling out of the sky. Snow, rain, sunshine, clouds, gale force winds – these are all weather.
Here are some animals being unimpressed with the weather.
Whether
This is the speculative one. You use whether when there is doubt or choice. Whether or not you want to do this depends on what you are writing about.