According to Archimedes' principle, a submerged object with a density lower than that of aqueous acid solution is more buoyant than a smaller one. In this work, a remarkable phenomenon is reported wherein a dissolving drop on a substrate rises in the water only after it has diminished to a much smaller size, though the buoyancy is smaller. The drop consisting of a polymer solution reacts with the acid in the surrounding, yielding a water-soluble product. During drop dissolution, water-rich microdroplets form within the drop, merging with the external aqueous phase along the drop-substrate boundary. Two key elements determine the drop rise dynamics. The first is the stick-jump behavior during drop dissolution. The second is that buoyancy exerts a strong enough force on the drop at an Archimedean number greater than 1, while the stick-jump behavior is ongoing. The time of the drop rise is controlled by the initial size and the reaction rate of the drop. This novel mechanism for programmable drop rise may be beneficial for many future applications, such as microfluidics, microrobotics, and device engineering where the spontaneous drop detachment may be utilized to trigger a cascade of events in a dense medium.