The words away, aweigh sound the same but have different meanings and spellings. Why do away, aweigh sound the same even though they are completely different words?
The answer is simple: away, aweigh are homophones of the English language.
From a particular thing or place: ran away from the lion; sent the children away to boarding school.
At or to a distance in space or time: We live a block away from the park.
At or by a considerable interval: away back in the 17th century; away off on the horizon.
In a different direction; aside: glanced away.
Nautical Hanging clear of the bottom. Used of an anchor.
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").