This study aims to develop and evaluate an obesity classification model using an Artificial Neural Network (ANN) combined with Explainable Artificial Intelligence (XAI) techniques based on SHAP (SHapley Additive exPlanations). The model was trained and tested using two different optimizers, Adaptive Moment Estimation (Adam) and Stochastic Gradient Descent (SGD), across multiple train-test ratios and epoch variations. The experimental results indicate that the Adam optimizer consistently outperformed SGD in terms of accuracy, loss value, and stability of evaluation metrics. The best performance was achieved with a 90:10 train-test ratio at 100 epochs, yielding an accuracy of 94.74%, a loss of 0.1899, precision, recall, and an f1-score of 0.95. To improve interpretability, SHAP was applied to identify the most influential features in the classification process. The analysis revealed that features such as Weight, Height, Gender, and Age significantly contribute to the model's predictions. Based on the SHAP interpretation, feature selection was conducted using the top nine features with the highest SHAP values. Retraining the ANN with these selected features resulted in improved performance, achieving 98.56% accuracy, a loss of 0.0638, and a precision, recall, and F1-score of 0.99 . These findings demonstrate that integrating XAI with ANN not only enhances transparency and interpretability but also boosts classification performance and computational efficiency. This approach shows strong potential for supporting decision-making in healthcare, particularly for early detection and intervention in cases related to obesity.