Studying blazar radio variability on timescales ranging from months to years provides information on the sub-parsec-scale structures of the jets, and the physics of the central active galactic nuclei. In this study, we focus on the radio variability of 1158 blazars observed at 15 GHz through the Owens Valley Radio Observatory Blazar Monitoring Program, where these sources have been observed about twice a week for over a decade. We investigate the dependence of the variability amplitudes and timescales, derived using a simple model fit to the structure function, on the milliarcsecond radio core sizes measured by Very Long Baseline Interferometry. The most compact sources exhibit larger variability amplitudes and shorter variability timescales than the more extended sources; this could be explained by light travel-time effects.