The widespread dissemination of health misinformation on social media is a significant threat for public health. Traditional machine learning approaches rely on manual feature engineering and often fail to perform on unseen data. Transformer-based models deliver superior performance but have high computational cost. This study evaluates lightweight transformer architecture: DistilBERT, TinyBERT, ALBERT, and ELECTRA, for classifying health misinformation. We introduce an inference-aware optimization framework using Optuna to determine model-specific hyperparameters. ALBERT achieves the highest accuracy (94.61%), whereas DistilBERT offers the best trade-off between accuracy and resource efficiency (92.97%). The results show that lightweight transformer models enable scalable, real-time health misinformation detection, offering a practical transition from traditional machine learning pipelines to more cutting-edge resource conscious systems.