Resistance spot welding is central to automotive manufacturing, yet real-time monitoring is often hindered by the rarity of defect samples and the high computational demands of multimodal sensing. This study proposes a lightweight physics-guided residual learning framework designed for high-precision weld classification with the potential for edge-level deployment. Unlike traditional black-box models, this architecture utilizes a dedicated physics branch based on the Joule heating law to establish a baseline, while a residual neural branch captures complex, non-linear anomalies. This hybrid approach enables the model to remain grounded in physical reality. This strategy achieves an overall classification accuracy of 95% and a macro F1-score of 0.82, significantly improving the recall of critical "Explode" defects to 81%. By prioritizing the detection of catastrophic failures while maintaining 98% precision for healthy welds, the model presents a scenario of evaluating safety without compromising industrial throughput. Furthermore, to study its applicability for factory-floor integration, the model was optimized via INT8 quantization, achieving a 3.5x compression ratio with minimal impact on diagnostic integrity. The results demonstrate that embedding the domain-specific physical constraints not only presents a scenario of model reliability in safety-critical applications but also enables the deployment of sophisticated AI diagnostics on low-power industrial edge controllers. Furthermore, the goal is to propose a lightweight model for industrial settings where expensive imaging hardware is unavailable or economically impractical. The model is inherently designed for simplistic deployment in small and medium-scale manufacturing environments, such as monitoring localized spot-welding parameters in Tier-2 automotive component assembly lines. This framework is also applicable to production lines requiring rapid quality control without a major infrastructure overhaul; for instance, it can be deployed onto standard programmable logic controllers in automotive supplier factories or small-scale metal stamping shops.