Wearable medical sensors (WMSs) are revolutionizing smart healthcare by enabling continuous, real-time monitoring of user physiological signals, especially in the field of consumer healthcare. The integration of WMSs and modern machine learning (ML) enables unprecedented solutions to efficient early-stage disease detection. Despite the success of Transformers in various fields, their application to sensitive domains, such as smart healthcare, remains underexplored due to limited data accessibility and privacy concerns. To bridge the gap between Transformer-based foundation models and WMS-based disease detection, we propose COMFORT, a continual fine-tuning framework for foundation models targeted at consumer healthcare. COMFORT introduces a novel approach for pre-training a Transformer-based foundation model on a large dataset of physiological signals exclusively collected from healthy individuals with commercially available WMSs. We adopt a masked data modeling (MDM) objective to pre-train this health foundation model. We then fine-tune the model using various parameter-efficient fine-tuning (PEFT) methods, such as low-rank adaptation (LoRA) and its variants, to adapt it to various downstream disease detection tasks that rely on WMS data. In addition, COMFORT continually stores the low-rank decomposition matrices obtained from the PEFT algorithms to construct a library for multi-disease detection. The COMFORT library enables scalable and memory-efficient disease detection on edge devices. Our experimental results demonstrate that COMFORT achieves highly competitive performance while reducing memory overhead by up to 52% relative to conventional methods. Thus, COMFORT paves the way for personalized and proactive solutions to efficient and effective early-stage disease detection for consumer healthcare.