Studies of motor generalization usually perturb hand reaches by distorting visual feedback with virtual reality or by applying forces with a robotic manipulandum. Whereas such perturbations are useful for studying how the central nervous system adapts and generalizes to novel dynamics, they are rarely encountered in daily life. The most common perturbations that we experience are changes in the weights of objects that we hold. Here, we use a center-out, free-reaching task, in which we can manipulate the weight of a participant's hand to examine adaptation and generalization following naturalistic perturbations. In both trial-by-trial paradigms and block-based paradigms, we find that learning converges rapidly (on a timescale of approximately two trials), and this learning generalizes mostly to movements in nearby directions with a unimodal pattern. However, contrary to studies using more artificial perturbations, we find that the generalization has a strong global component. Furthermore, the generalization is enhanced with repeated exposure of the same perturbation. These results suggest that the familiarity of a perturbation is a major factor in movement generalization and that several theories of the neural control of movement, based on perturbations applied by robots or in virtual reality, may need to be extended by incorporating prior influence that is characterized by the familiarity of the perturbation.