If you are a woman is really overweight and has facial hair growing and she loses the weight will the facial hair go?

Facial hair could likely be an over active thyroid problem so you have to get your thyroid balanced if that is what it is
Avoid broccoli, cabbage, brussels sprouts, cauliflower, kale, spinach, turnips, soy, beans, and mustard greens, refined foods, sugar, dairy products, wheat, caffeine, alcohol. See if that helps any
Also get your iodine level checked. Do not do if you are allergic to iodine

Apply Tincture of Iodine to your skin is the most efficient (as well as most economical) method of determining a metabolic deficiency of iodine. It is a "test" as well as a "treatment". If the "brown" stain fades in 24 hours or less, it indicates that Iodine is not sufficient to normalize thyroid secretion to the cells. Even if you are taking thyroid orally to stimulate your own thyroid, lack of iodine will interfere with your body's ability to properly utilize it.

If you're asking simply if there's a connection solely between a woman's weight + her facial hair... the answer is no. Is there a certain hormone/chemical imbalance that affects both? Then yes.

But just because a woman gains weight doesn't mean she'll start growing facial hair.