Recent work has uncovered a strong correlation between Wide-field Infrared Survey Explorer (WISE) 12 micron (W3) and CO luminosity in nearby galaxies. The W3 band includes several polycyclic aromatic hydrocarbon (PAH) emission features, and thus this correlation suggests that there may be a physical link between PAHs and molecular gas. To better understand this correlation, we present a spatially resolved (kpc resolution) study of the W3-CO relationship in galaxies from the Extragalactic Database for Galaxy Evolution (EDGE) CO survey. We match the angular resolution of the EDGE CO data to that of W3 images to characterize the pixel-by-pixel W3-CO correlation. We find that the correlation is strong within each galaxy and that there are significant offsets from galaxy-to-galaxy. We developed a multi-linear regression and model selection algorithm and find that the global UV emission (which is responsible for exciting PAH molecules) is the dominant driver of galaxy-to-galaxy differences. These results improve our understanding of the relationship between molecular gas and mid-infrared emission, provide a spatially resolved estimator of molecular gas, and motivate future work combining spatially resolved mid-infrared spectroscopy from JWST and CO measurements from ALMA.