Genetic effects on changes in human traits over time are understudied and may have important pathophysiological impact. We propose a framework that enables data quality control, implements mixed models to evaluate trajectories of change in traits, and estimates phenotypes to identify age-varying genetic effects in genome-wide association studies (GWASs). Using childhood body mass index (BMI) as an example, we included 71,336 participants from six cohorts and estimated the slope and area under the BMI curve within four time periods (infancy, early childhood, late childhood and adolescence) for each participant, in addition to the age and BMI at the adiposity peak and the adiposity rebound. GWAS on each of the estimated phenotypes identified 28 genome-wide significant variants at 13 loci across the 12 estimated phenotypes, one of which was novel (in DAOA) and had not been previously associated with childhood or adult BMI. Genetic studies of changes in human traits over time could uncover novel biological mechanisms influencing quantitative traits.