Lose weight is the correct phrase. Lose and loose have different pronunciations, meanings, and grammatical functions. Lose means to no longer have something which you had previously.
Lose has a long “o” and a “z” sound. It is a verb that means “suffer loss” or “misplace.”
Loose also has a long “o” sound, but the “s” is soft. It is an adjective or adverb that means “not tight” or “not secure.” Occasionally loose is used as a verb meaning “release.”
You used to have some weight which you no longer have, so you lose weight. It means that your clothes will now be loose as they are no longer so tight.