Why has my voice been hoarse for weeks?
Hoarseness means the vocal cords are not closing and vibrating the way they normally do. Swelling, a small growth on the cord, dryness, muscular strain, inflammation from reflux, or a nerve that is not working fully can all produce a similar sound. The voice itself cannot tell you which of these it is.
This is why the three-week mark matters. A voice that goes hoarse after a cold or a long weekend usually recovers within days. Hoarseness that carries on beyond roughly three weeks should be looked at, so that the cause is identified rather than assumed.