The Weddell Gyre is one of the dominant features of the Southern Ocean circulation and its dynamics have been linked to processes of climatic relevance. Variability in the strength of the gyre's horizontal transport has been linked to heat transport towards the Antarctic margins and changes in the properties and rates of export of bottom waters from the Weddell Sea region to the abyssal global ocean. However, the precise physical mechanisms that force variability in the Weddell's lateral circulation across different timescales remain unknown. In this study, we use a barotropic vorticity budget from a high-resolution model simulation to attribute changes in gyre strength to variability in possible driving processes. We find that the Weddell Gyre's circulation is sensitive to bottom friction associated with the overflowing dense waters at its western boundary. In particular, an increase in the production of dense waters at the southwestern continental shelf strengthens the bottom flow at the gyre's western boundary, yet this drives a weakening of the depth-integrated barotropic circulation via increased bottom friction. Strengthening surface winds initially accelerates the gyre, but within a few years the response reverses once dense water production and export increases. These results reveal that the gyre can weaken in response to stronger surface winds, putting into question the traditional assumption of a direct relationship between surface stress and gyre strength in regions where overflowing dense water forms part of the depth-integrated flow.