The number of obese children and adolescents (aged five to 19 years) worldwide has risen tenfold in the past four decades. If current trends continue, more children and adolescents will be obese than moderately or severely underweight by 2022, according to a new study led by Imperial College London and WHO.

Trends in childhood obesity and underweight. Source: The Lancet
The paper is available at
http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(17)32129-3/fulltext#sec1
More than 1000 contributors participated in the study, which looked at body mass index (BMI) and how obesity has changed worldwide from 1975 to 2016. The study analysed weight and height measurements from nearly 130 million people aged over five years. It provides a complete picture of trends in mean BMI and prevalence of BMI categories that cover the underweight to obese range among children and adolescents aged 5–19 years, for all countries in the world with the longest observation period, and compares trends with those of adults.
Obesity rates in the world’s children and adolescents increased from less than 1% (equivalent to five million girls and six million boys) in 1975 to nearly 6% in girls (50 million) and nearly 8% in boys (74 million) in 2016. Combined, the number of obese five to 19 year olds rose more than tenfold globally, from 11 million in 1975 to 124 million in 2016. An additional 213 million were overweight in 2016 but fell below the threshold for obesity.
Children and adolescents have rapidly transitioned from mostly underweight to mostly overweight in many middle-income countries, including in East Asia, Latin America and the Caribbean. More recently, overweight and obesity levels have plateaued in higher income countries, although obesity levels remain unacceptably high. Among high-income countries, the United States of America had the highest obesity rates for girls and boys.
The number of obese adults increased from 100 million in 1975 (69 million women, 31 million men) to 671 million in 2016 (390 million women, 281 million men). Another 1.3 billion adults were overweight, but fell below the threshold for obesity. Here are maps of adult obesity levels in 2016 from the NCD-Risc website (see link below).

Prevalence of obesity in adult males in 2016. Source: NCD-RisC

Prevalence of obesity in adult females in 2016. Source: NCD-RisC
Detailed results can be explored using dynamic visualisations and downloaded from the NCD-RisC website at