Using county-level data from the United States, we assessed allometric scaling relationships of coronavirus disease (COVID-19) cases, deaths and age structure within and across the first four major waves of the pandemic (wild-type, alpha, delta, omicron). Results generally indicate that the burden of cases disproportionately impacted larger-sized counties, while the burden of deaths disproportionately impacted smaller counties. This may be partially due to multiple interacting social mechanisms, including a higher proportion of older adults who live in smaller counties. Moreover, these likely social mechanisms interacting with vaccinations and virus waves created a dynamic pattern whereby the rate and magnitude of infections and deaths were population- and time-dependent. Our results offer a novel perspective on the scaling dynamics of infectious diseases, highlighting how both the rate and magnitude of COVID-19 cases and deaths scale differently across counties. Population size and age structure are key factors in predicting disease burden. Our findings have practical implications, suggesting that scaling-informed public health policies could more effectively allocate resources and interventions to mitigate the impact of future epidemics across heterogeneous populations.