An hourglass is known to become slightly heavier while the sand is falling. We quantitatively reproduced this minute weight change through numerical simulation. By treating the hourglass as a mechanical system of coupled variable-mass objects, we find that two effects contribute equally to the weight variation: the linear change in the thickness of the sand layers and the progressive shortening of the free-fall distance of the sand grains. Based on this analysis, we developed a discrete element simulation using the soft-sphere approach. In this model, sand grains fall at a constant rate and accumulate into multiple vertical piles. The simulation, implemented in Processing, can be run on a standard notebook PC.