An imaging-integrated microfluidic cell volume sensor was used to evaluate the volumetric growth rate of single cells from a Saccharomyces cerevisiae population exhibiting two phenotypic expression states of the PDR5 gene. This gene grants multidrug resistance by transcribing a membrane transporter capable of pumping out cytotoxic compounds from the cell. Utilizing fluorescent markers, single cells were isolated and trapped, then their growth rates were measured in two on-chip environments: rich media and media dosed with the antibiotic cycloheximide. Approximating growth rates to first-order, we assessed the fitness of individual cells and found that those with low PDR5 expression had higher fitness in rich media whereas cells with high PDR5 expression had higher fitness in the presence of the drug. Moreover, the drug dramatically reduced the fitness of cells with low PDR5 expression but had comparatively minimal impact on the fitness of cells with high PDR5 expression. Our experiments show the utility of this imaging-integrated microfluidic cell volume sensor for high-resolution, single-cell analysis, as well as its potential application for studies that characterize and compare the fitness and morphology of individual cells from heterogeneous populations under different growth conditions.