The words might, mite sound the same but have different meanings and spellings. Why do might, mite sound the same even though they are completely different words?
The answer is simple: might, mite are homophones of the English language.
The power, force, or influence held by a person or group.
Strength or ability to do something. See Synonyms at strength. See Regional Note at powerful.
Used to indicate a condition or state contrary to fact: She might help if she knew the truth.
Any of various small or minute arachnids of the order Acarina that are often parasitic on animals and plants, infest stored food products, and in some species transmit disease.
A very small contribution or amount of money.
A widow's mite.
A very small object, creature, or particle.
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").