The words ways, weighs sound the same but have different meanings and spellings. Why do ways, weighs sound the same even though they are completely different words?
The answer is simple: ways, weighs are homophones of the English language.
Informal Variant of way. See Usage Note at way.
Third-person singular simple present indicative form of weigh.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License 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").