This paper presents an optimized Field-Programmable Gate Array (FPGA) implementation of a Ballistocardiogram (BCG) signal filtering scheme incorporating dynamic weight updates. BCG signals provide valuable physiological information but are often contaminated with noise. To enhance the accuracy of BCG signal analysis, we propose a novel FPGA-based filtering approach that dynamically adjusts filter weights. Our implementation leverages the reconfigurable nature of FPGAs to adaptively modify filter coefficients, resulting in improved signal quality and enhanced diagnostic capabilities. We discuss the design, synthesis, and evaluation of our FPGA-based system, demonstrating significant improvements in BCG signal fidelity and robustness.