Recently, the potential of lightweight models for resource-constrained scenarios has garnered significant attention, particularly in safety-critical tasks such as bio-electrical signal classification and B-ultrasound-assisted diagnostic. These tasks are frequently affected by environmental noise due to patient movement artifacts and inherent device noise, which pose significant challenges for lightweight models (e.g., deep binary neural networks (DBNNs)) to perform robust inference. A pertinent question arises: can a well-trained DBNN effectively resist environmental noise during inference? In this study, we find that the DBNN's robustness vulnerability comes from the binary weights and scaling factors. Drawing upon theoretical insights, we propose L1-infinite norm constraints for binary weights and scaling factors, which yield a tighter upper bound compared to existing state-of-the-art (SOTA) methods. Finally, visualization studies show that our approach introduces minimal noise perturbations at the periphery of the feature maps. Our approach outperforms the SOTA method, as validated by several experiments conducted on the bio-electrical and image classification datasets. We hope our findings can raise awareness among researchers about the environmental noise robustness of DBNNs.