Obesity is a common issue in modern societies today that can lead to significantly reduced quality of life. Existing research on investigating obesity-related neurological characteristics is limited to traditional approaches such as significance testing and regression. These approaches may require certain neurological assumptions to be made and may struggle to handle the complexity and non-linear relationships within the high-dimensional electroencephalography (EEG) data. In this study, we propose a deep learning-based approach for extracting features from resting-state EEG signals to classify obesity-related brain activity. Specifically, we employ a Variational Autoencoder (VAE) to learn robust feature representations from EEG data, followed by classification using a 1-D convolutional neural network (CNN). By comparing our approach with benchmark models, we demonstrate the efficiency of VAE in feature extraction, evidenced by significantly improved classification accuracies, enhanced visualizations, and reduced impurity measures in the learned feature representations.