My daughter is 13 yo. she has not started her period yet, she is obese, she has recently developed darkened mustache hair. what's going on?

Hard to say: Lack of menses at 13 is not unusual but lack of any breast tissue would deserve a workup.Sometimes excess weight can mimic breast tissue.Menses will usually follow early breast development by 2-3 yrs at the latest or age 15. Darkening of hair is usually due to hormonal influence from the adrenal glands. Your doc could pursue these issues for you.