An issue of continued debate in the visuomotor control literature surrounds whether a 2D object serves as a representative proxy for a 3D object in understanding the nature of the visual information supporting grasping control. In an effort to reconcile this issue, we examined the extent to which aperture profiles for grasping 2D and 3D objects adheres to, or violates, the psychophysical properties of Weber's law. Specifically, participants grasped differently sized 2D and 3D objects (20, 30, 40, and 50 mm of width) and we computed the just-noticeable-difference scores associated with aperture profiles at decile increments of normalized grasping time. The aperture profiles for 2D objects showed an early through late (i.e., 10% through 90%) adherence to Weber's law, whereas the late stages of grasping 3D objects (i.e., greater than 50% of grasping time) produced a fundamental violation of the law's principles. As such, results suggest that grasping a 2D object is a top-down and cognitive task mediated via relative visual information. In contrast, the enriched shape information provided by a 3D object (i.e., stereoscopic vergence and disparity cues) allows for later aperture specification via absolute (Euclidean) visual information. Most notably, our results establish that the dimensional properties of an object influence the visual information mediating motor output, and further indicate that 2D and 3D objects are not representative proxies for one another in understanding the visual control of grasping. (Contains 1 table and 2 figures.)