Increasing atmospheric CO2 and surface temperatures should increase carbonate and silicate weathering rates, directly via warming, and indirectly via the CO2 fertilization effect enhancing plant productivity. Enhanced weathering should in turn increase alkalinity input to the ocean and accelerate long-term CO2 uptake. We added silicate and carbonate weathering and carbonate sediments to an existing global carbon cycle and surface temperature model and subjected it to a range of long-term fossil fuel emissions scenarios, spanning 1100--15,000 GtC in total. Emissions of ≥7350 GtC dissolve all carbonate sediments, and enhanced carbonate and silicate weathering accelerate subsequent CO2 removal from the atmosphere by up to a factor of 4. For 1100--4000 GtC emissions, enhanced weathering accelerates CO2 removal by a factor of 1.5--2.5. However, it takes >1 Myr for silicate weathering to stabilize atmospheric CO2. If land use tends to suppress vegetation and weathering rates on this timescale, then CO2 will stabilize above preindustrial levels.