Quantitative Structure-Property Relationship (QSPR) analysis plays a crucialrole in predicting physicochemical properties and biological activities ofpharmaceutical compounds, aiding in drug design and optimization. This studyfocuses on leveraging QSPR within the framework of vertex and edge weighted(VEW) molecular graphs, exploring their significance in drug research. Byexamining 48 drugs in used in the treatment of various cancers and theirphysicochemical properties, previous studies serve as a foundation for ourresearch. Introducing a novel methodology for computing vertex and edgeweights, exemplified by the drug Busulfan, we highlight the importance ofconsidering atomic properties and inter-bond dynamics. Statistical analysis,employing linear regression models, reveals enhanced correlations betweentopological indices and physicochemical properties of drugs. Comparison withprevious studies on unweighted molecular graphs highlights the enhancementsachieved with our approach.