If you typically screen kids for height/weight/BMI, and have some sort of follow-up letter that you send home after these screenings, then I think that's all I would do, and make sure to include my phone number if mom wants to call and talk.
If the little girl is demonstrating inappropriate behaviors around mealtime, like stealing food from kids or shoving food into her mouth, then that could be addressed with mom. It could also be used as a gateway conversation to discuss her health.
I know we all want kids to be their healthiest and happiest, but honestly, I don't feel that I'm the appropriate healthcare provider to address weight issues with a parent. Compared to the kid's pedi, I'm a stranger who does not have a long-standing professional relationship with the parent.
Side note: we check each kid's height, weight, and BMI at the start of the year, and send home letters with that information + available resources if a parent would like help. One parent was so offended at her child being categorized as obese, she actually got the pedi to write a letter saying he's aware the kid is obese but it's fine.