Categories of weight status in adults and children include underweight (body mass index (BMI) < 18.0 kg/m2 for adults and < 5th age-sex-specific percentile for children), normal weight (BMI 18.0 to < 25.0 kg/m2 for adults and 5th to < 85th percentile for children), overweight (BMI 25.0 to < 30.0 kg/m2 for adults and 85
There is a reference developed in 2006 by the Epinut research group from the Complutense University of Madrid but it is based on Spanish children. It provides percentiles by sex and age based on the 4 basic skinfolds and the equations from Durning & Womersley, Siri, and Slaughter. Here is the link to the article: https://www.analesdepediatria.org/es-pdf-13090892
Besides, there is a classical classification proposed by Westrate and Deuremberg in 1989 in where they stated that the presence of obesity in prepubescent children exists when the %body fat obtained by anthropometry is greater than 30% without distinction of age. This is the link to the article: https://academic.oup.com/ajcn/article-abstract/50/5/1104/4695440
I hope this could be useful for you. If anyone knows any other reference I'd also appreciate reading it.
Children between 6-8 years of age average 13-15% fat for boys and 16-118% fat for girls. For postpubescent youth 14-16 years of age, boys average 10-12% fat and girls average 21-23% fat. By young adulthood, males average 13% fat and females average 24% fat using anthropometric measurement.