Menarche (the start of a girl's menstrual period) is not dependent upon weight alone but the amount of body fat, height and weight all play a role in determining the start of puberty. A woman's genes and the age her mother began her period is a major factor in determining when a girl will have her period. There are other physiologic and environmental events that also matter and girls develop at different rates depending upon geography and ethnicity.
Every girl develops at a different rate but most girls have their first period by age 15 or 16. In the United States the median age of menarche is 12.43 years and 90 percent of all girls have their period by the time they are 14 years old. These statistics have not changed in the last 40 years in the United States.