The words we've, weave sound the same but have different meanings and spellings. Why do we've, weave sound the same even though they are completely different words?
The answer is simple: we've, weave are homophones of the English language.
Contraction of we have.
To spin (a web, for example).
To make (cloth) by interlacing the threads of the weft and the warp on a loom.
To interlace (threads, for example) into cloth.
To construct by interlacing or interweaving strips or strands of material: weave a basket.
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").