The size-weight illusion (SWI) pertains to the experience of perceiving the smaller of two equally weighted objects as heavier. Competing theories to explain the illusion can be generally grouped into cognitive and sensory theories, which place more importance on top-down processing of cognitive expectations and bottom-up processing of sensory information about the size and weight of objects, respectively. The current study examined the relative contribution of these two general explanations. This was done by varying the amounts of cognitive load in a dual-task and the quality of somatosensory feedback by wearing or not wearing gloves. Participants placed their hands through a curtain inside a box so they could not see the test objects. Inside the box, they were presented with either a small or large sphere of varying weights, which they explored manually without vision. Participants provided magnitude estimates about each object's weight in four experimental conditions (no-load with gloves, no-load without gloves, low-load without gloves, and high-load without gloves). The dual-task involved the visual presentation of a cross on a computer monitor that changed in both colour and orientation. With foot pedals, the participants responded to a target colour and / or orientation, which varied across conditions, while they hefted an object. Some conditions were designed to be more cognitively taxing than others (high-load > low-load > no-load conditions). The results revealed that the strength of the SWI diminished when participants wore the gloves but did not change as cognitive load increased on the dual-task. We conclude that the illusion is more influenced by bottom-up sensory than top-down cognitive processes.