Obesity is a pressing global health challenge that necessitates robust and interpretable models for predicting Body Mass Index (BMI). In this study, we utilized data from the Korea National Health and Nutrition Examination Survey (KNHANES) to evaluate multiple machine learning models for both BMI regression and binary classification (using threshold 25 kg/m). Among the tested models, the XGBRegressor achieved the highest area under the curve (AUC) in binary classification. However, interpretability remains critical in clinical applications.To enhance transparency, we employed a knowledge distillation approach, using the XGBRegressor as the teacher model and training a single DecisionTreeRegressor as the student model. This distillation process significantly improved the decision tree's performance compared to training it directly on the dataset. Furthermore, the distilled model enabled interpretable, rule-based predictions, highlighting key obesity-related features such as insulin resistance (HOMA-IR).Clinical relevance- By providing a transparent decision-making process, the distilled model aids clinicians in identifying critical obesity-related factors, such as insulin resistance (HOMA-IR). This enhanced interpretability facilitates more targeted and data-driven interventions for obesity management and associated health risks.