weighted, waited

The words weighted, waited sound the same but have different meanings and spellings. Why do weighted, waited sound the same even though they are completely different words?

The answer is simple: weighted, waited are homophones of the English language.

waited
  1. :: verb

    Simple past tense and past participle of wait.

weighted
  1. :: adjective

    Made heavy or heavier by the addition of something: a weighted base.

  2. :: adjective

    Statistics Adjusted to reflect value or proportion: a weighted average.

Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.

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About Homophones

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").