Small water droplets or particles located at an oil meniscus typically climb the meniscus due to unbalanced capillary forces. Here, we introduce a size-dependent reversal of this meniscus-climbing behavior, where upon cooling of the underlying substrate, droplets of different sizes concurrently ascend and descend the meniscus. We show that microscopic Marangoni convection cells within the oil meniscus are responsible for this phenomenon. While dynamics of relatively larger water microdroplets are still dominated by unbalanced capillary forces and hence ascend the meniscus, smaller droplets are carried by the surface flow and consequently descend the meniscus. We further demonstrate that the magnitude and direction of the convection cells depend on the meniscus geometry and the substrate temperature and introduce a modified Marangoni number that well predicts their strength. Our findings provide a new approach to manipulating droplets on a liquid meniscus that could have applications in material self-assembly, biological sensing and testing, or phase change heat transfer.