If a weight is applied to a finger and the subject asked to produce the same force, the subject generates a force larger than the weight. That is, subjects overestimate the force applied by an external target when matching it. Details of this force overestimation are not well understood. We show that subjects overestimate small target weights, but not larger ones. Furthermore we show for the first time that the force overestimation consists of two components. The first component is a constant. The second component depends on the precise magnitude of the weight and is only present when subjects hold the target weight against gravity. We suggest that the two components are generated in different phases of the force-matching task, are due to different processes, and must have an influence on all proprioceptive judgements of force.