Conventional miRNA-based diagnostic methods often treat all biomarkers equally, overlooking the fact that each miRNA contributes differently to disease classification. This differential diagnostic importance is captured by the concept of Cancerous Diagnostic Valence (CDV)-a metric that quantifies both the direction (oncogenic or protective) and magnitude of each miRNA's association with cancer. Here, we introduce a polymerase-based DNA molecular computing system that directly encodes and integrates CDVs to perform weighted molecular classification of non-small cell lung cancer (NSCLC). By coupling DNA polymerase-mediated strand extension and displacement (PB-DSD and cascade PB-DSD), the system translates miRNA inputs into proportional molecular signals spanning a wide CDV range (1-25), with minimal probe complexity. Seven NSCLC-related miRNAs with machine learning-derived CDVs were used to construct a diagnostic classifier, achieving 95% accuracy in tissue and 90% in plasma samples. Compared to conventional toehold strand displacement systems, this approach offers broader scalability, lower background interference, and more accurate diagnostic logic. Furthermore, we demonstrate its utility for therapeutic monitoring by tracking drug-induced shifts in CDV-weighted miRNA profiles in tumor-bearing mice treated with allicin and curcumin. This work establishes a molecularly programmable and biologically informed diagnostic platform that advances the precision and interpretability of miRNA-based cancer diagnostics.