Triple oxygen isotope (Delta O-17 with delta O-18) signals of H2O and O-2 found in sulfate of oxidative weathering origin offer promising constraints on modern and ancient weathering, hydrology, atmospheric gas concentrations, and bioproductivity. However, interpretations of the sulfate-water-O-2 system rely on assuming fixed oxygen-isotope fractionations between sulfate and water, which, contrastingly, are shown to vary widely in sign and amplitude. Instead, here we anchor sulfate-water-O-2 triple oxygen isotope systematics on the homogeneous composition of atmospheric O(2 )with empirical constraints and modeling. Our resulting framework does not require a priori assumptions of the O-2- versus H2O-oxygen ratio in sulfate and accounts for the signals of mass-dependent and mass-independent fractionation in the Delta O-17 and delta O-18 of sulfate's O-2-oxygen source. Within this framework, new Delta O-17 measurements of sulfate constrain similar to 2.3 Ga Paleoproterozoic gross primary productivity to between 6 and 160 times present-day levels, with important implications for the biological carbon cycle response to high CO2 concentrations prevalent on the early Earth.