Estimates of the Weddell Gyre transport vary widely between climate simulations. Here, we investigate if inter-model variability can originate from differences in the horizontal resolution of the ocean model. We run an idealized model of the Weddell Gyre at eddy-parametrized, eddy-permitting, and eddy-rich resolutions and find that the gyre is very sensitive to horizontal resolution and the gyre transport is largest at eddy-permitting resolutions. The eddy-permitting simulations have the largest horizontal density gradients and the weakest stratification over the gyre basin. The large horizontal density gradients induce a significant thermal wind transport and increase the mean available potential energy for mesoscale eddies. Explicit eddies in simulations intensify the bottom circulation of the gyre via non-linear dynamics. If climate models adopt horizontal resolutions that the Weddell Gyre is most sensitive to, then simulations of the Weddell Gyre could become more disparate.