Childhood obesity is a major public health concern. Multidisciplinary pediatric weight management programs are considered standard treatment for children with obesity and severe obesity who are not able to be successfully managed in the primary care setting; however, high drop-out rates (referred to as attrition) are a major hurdle in delivering successful interventions. Predicting attrition patterns can help providers to reduce the attrition rates. Previous work has mainly focused on finding static predictors of attrition using statistical analysis methods. In this study, we present a machine learning model to predict a) the likelihood of attrition, and b) the change in body-mass index (BMI) percentile of children, at different time points after joining a weight management program. We use a five-year dataset containing the information related to around 4,550 children that we have compiled using data from the Nemours Pediatric Weight Management program. Our models show strong prediction performance as determined by high AUROC scores across different tasks (average AUROC of 0.75 for predicting attrition, and 0.73 for predicting weight outcomes). Additionally, we report the top features predicting attrition and weight outcomes in a series of explanatory experiments.