In size-weight (SW) illusions, people learn to scale their fingertip forces for lifting small and big objects of equal weight even though they fail to learn perceptually that both objects have the same weight. The question then arises as to what the separate neural mechanisms are for determining the perceived heaviness of objects and the predicted weight of these objects during lifting. To answer this question, we used fMRI to first identify areas that code for the size, weight, and density of objects using an adaptation paradigm. We then contrasted BOLD in the SW illusion condition in which subjects falsely perceived the smaller of two equally weighted objects as heavier versus a condition in which size and weight did not differ between objects. Sensory areas in the parietal and temporal cortex adapted to the size of objects and the primary motor area (M1) contralateral to the lifting hand adapted to the weight of objects. The ventral premotor area (PMv), which did not adapt to either the size or the weight of objects, adapted instead to the density of objects, and responded more when subjects falsely perceived differences in weight between objects in the SW illusion condition. Taken together, we conclude that the real-world properties of objects, such as size and weight, are computed by sensory areas and by M1 respectively, whereas the perceived heaviness of objects, presumably based on their apparent density, is computed by PMv, a higher-order area well placed to integrate sensory information about the size of objects and the weight of objects.