Weather vs. Whether
Use weather when referring to rain, lightning, snow… all of those meteorological occurrences that you hope will result in school being canceled tomorrow.
Use whether when you're talking about alternatives and options.
"Zoe's flight to Barbados was delayed for three hours due to inclement weather."
We hope she got some free snacks out of the ordeal. There's nothing that a tiny bag of exactly nine mini-pretzels can't fix. Weather's the way to go here since we're talking about atmospheric changes like wind or thunderstorms.
"When my cat, Mrs. Paddleball, turned my computer off with her tail, I didn't know whether to laugh or to cry."
We can understand the dilemma: on the one hand, that's an impressive feat for a cat. On the other hand, if you haven't saved your game recently… ouch. Here, the speaker's talking about two options—laughing or crying—so whether is the right choice.
"Please let me know whether you're bringing a date to the wedding."
That's just good manners. What's also good is using whether here since we're talking about two alternatives: bringing a date or not bringing a date.