If weight was correlated with puberty, I wouldn’t have had my period until I was about 17

I was underweight and the doctor said that the timing of puberty is mostly genetic, and I got my period at 13 just like my mom, aunts and grandmother. On the other hand, my sister and cousin were also underweight and didn’t get their periods until they were 16 and the doctors said that age 16 is when they start considering other medical problems if your period hasn’t arrived by then. We have a family history of being underweight and some of us had delayed puberty, so I spent a lot of time dealing with this as a kid. And I get it—the teasing is hard! I looked 3-4 years younger and smaller than my actual age, so also endured a lot of teasing.
My mom is a doctor and said that there’s evidence that being overweight releases additional hormones that cause early puberty, and doctors are seeing more signs of this. Not sure if any of this helps, but might be worth chatting with your pediatrician if you’re concerned.