The words way, weigh, whey sound the same but have different meanings and spellings. Why do way, weigh, whey sound the same even though they are completely different words?
The answer is simple: way, weigh, whey are homophones of the English language.
A road, path, or highway affording passage from one place to another.
An opening affording passage: This door is the only way into the attic.
Space to proceed: cleared the way for the parade.
Opportunity to advance: opened the way to peace.
To determine the weight of by or as if by using a scale or balance.
To measure or apportion (a certain quantity) by or as if by weight. Often used with out: weighed out a pound of cheese.
To balance in the mind in order to make a choice; ponder or evaluate: weighed the alternatives and decided to stay.
To choose carefully or deliberately: weigh one's words.
The watery part of milk that separates from the curds, as in the process of making cheese.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").