This study investigates the performance of machine learning models for seven-class obesity classification using Synthetic Minority Over-sampling Technique for Nominal and Continuous features (SMOTE-NC) and model-based feature selection. The UCI obesity dataset initially contained 2,111 records from Colombia, Peru, and Mexico. After removing 24 exact duplicates, 2,087 unique records were retained and divided using a stratified 80:20 training-test split. To prevent data leakage, SMOTE-NC was applied exclusively to the training folds within the cross-validation pipeline. Feature selection was performed using Random Forest-based SelectFromModel with a median importance threshold, reducing 31 encoded features to 16 selected features. Logistic Regression, Support Vector Machine, and Random Forest were evaluated using repeated stratified five-fold cross-validation with ten repetitions. The ablation analysis produced mean macro F1-scores of 93.21\% for the baseline, 93.27\% for SMOTE-NC only, 93.69\% for feature selection only, and 93.89\% for the combined SMOTE-NC and feature-selection pipeline. The combined pipeline significantly outperformed the baseline after Holm correction (adjusted $p < 0.001$), whereas SMOTE-NC alone did not produce a significant improvement (adjusted p = 0.527). After GridSearchCV optimization, Random Forest achieved 94.98\% accuracy and a macro F1-score of 94.84\% on the untouched test set. These findings demonstrate that the combined pipeline improves multiclass obesity classification, with feature selection providing the primary performance contribution and SMOTE-NC serving as a complementary class-balancing technique.