The weather outside is partly cloudy whether you like it that way or not. A wether, on the other hand, is a castrated sheep. You read that right.
Weather comes from the Old English weder, for basically, "air and sky." It used to refer to storms, but now the weather can be sunny, too. Ships that weather a storm get through it, just like people who weather something. Examples:
"Given the odd weather of late, you may be aware that we are in the midst of what could be a record-setting El Niño." (Washington Post)
"If you enter the theater of this novel, get set to weather some disorientation as soon as the lights dim." (Washington Post)
The word whether indicates a choice. You can decide whether to go to the movies. The "or not" isn't necessary because it's implied in the word whether. "Or not" can be added if it means, "regardless of whether," as in "We will play outside whether or not it snows." Here's Hamlet's famous choice:
"To be, or not to be? That is the question—
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles…"
Poor little wether. It's always jumping in for whether but wether is never a choice. It's always a sheep or a goat. The word pops up a lot, but these sentences actually get it right:
"He jumped up, and called to the shepherd— 'I say, old boy, let that bell wether of mine alone, will you?'" (Richard Cobbold)
"My shepherd's pipe can sound no deal, my wether's bell rings doleful knell." (William Henry Burr)
Weather refers to climate conditions and whether comes before a choice. As for wether, be careful. If you say "We're having great wether tonight," it might sound like you're serving castrated goat for dinner.