Infant obesity has become one of the most serious global health challenges of our time. The combined prevalence of overweight and obesity has rapidly increased worldwide during the last two decades, especially in some developing countries where obesity is reaching levels on a par with some industrialized countries, or even higher. This fast growth has occurred especially in countries in the midst of rapid social-economic transitions. Most international comparisons focus on the adult population while analyses focusing on the child population are more limited. Using the methodology developed by Phillips and Sul [1], this paper studies the worldwide evolution of infant body mass index (BMI), overweight and obesity prevalence for a large sample of countries during the period 1975-2016. Our results indicate that the figures for BMI or the prevalence of obesity in different countries do not converge, while the opposite is the case for overweight prevalence in children. Furthermore, there is a non-linear relationship between obesity and income or human capital, indicating that low and middle-income countries require a strong initiative for health policies targeting obesity prevention.