Argo floats provide both hydrographic and trajectory data, affording the opportunity to investigate surface to mid-depth ocean dynamics. Here, Argo float data are used to determine the absolute geostrophic velocity field of the upper 50–2000 m of the Weddell Gyre, from which the overall circulation pattern is investigated. The Weddell Gyre plays a pivotal role in the modification of climate by advecting heat towards the Antarctic ice shelves and by modifying the water masses that feed into the lowest limb of the global ocean overturning circulation. Warm Deep Water, the source water mass that delivers heat to the Weddell Gyre, is conveniently located within the upper 2000 m domain covered by the floats; we investigate its volume transport as it circulates the gyre. Full depth volume transports are estimated by applying a quadratic function to extrapolate the relative dynamic height field component to the full ocean depth, using CTD profiles from ship-based surveys to determine an extrapolation error. Major new insights are provided by this study. There is an established double-gyre structure to the circulation, with a strong eastern cell and a weaker western cell. Regional variation of the baroclinic component of the flow field is revealed, indicating a northeast-to-southwest reduction in the baroclinic flow, along with a strong meridional gradient of baroclinic flow along the northern limb of the gyre, especially east of ∼25°W. The zonal mean gyre strength away from the shelf edge is 32 ± 5 Sv (1 Sv = 1 × 106 m3 s−1), of which 13 ± 3 Sv are associated with the advection of Warm Deep Water. There is a considerable amount of recirculation within the gyre interior, where water does not traverse the full zonal extent of the gyre. The recirculation is stronger in the eastern cell of the observed double-gyre structure. The interior circulation cells partly explain the large variations in previous gyre strength estimates. We provide an extensive review of previous estimates in context of the new results obtained.