The words weak, week sound the same but have different meanings and spellings. Why do weak, week sound the same even though they are completely different words?
The answer is simple: weak, week are homophones of the English language.
Lacking physical strength, energy, or vigor; feeble.
Likely to fail under pressure, stress, or strain; lacking resistance: a weak link in a chain.
Lacking firmness of character or strength of will.
Lacking the proper strength or amount of ingredients: weak coffee.
A period of seven days: a week of rain.
A seven-day calendar period, especially one starting with Sunday and continuing through Saturday: this week.
A week designated by an event or holiday occurring within it: commencement week.
A week dedicated to a particular cause or institution: Home Safety Week.
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").