Photoacids and photobases constitute a class of molecules that upon absorption of light undergoes a reversible change in acidity, i.e. pKa. Knowledge of the excited-state pKa value, pKa*, is critical for predicting excited-state proton-transfer behavior. A reasonable approximation of pKa* is possible using the Förster cycle analysis, but only when the ground-state pKa is known. This poses a challenge for the study of weak photoacids (photobases) with less acidic (basic) excited states (pKa* (pKb*) > 7), because ground-state pKa (pKb) values are >14, making it difficult to quantify them accurately in water. Another method to determine pKa* relies on acid-base titrations with photoluminescence detection and Henderson-Hasselbalch analysis. This method requires that the acid dissociation reaction involving the thermally equilibrated electronic excited state reaches chemical quasi-equilibrium, which does not occur for weak photoacids (photobases) due to slow rates of excited-state proton transfer. Herein, we report a method to overcome these limitations. We demonstrate that liquid water and aqueous hydroxide are unique proton-accepting quenchers of excited-state photoacids. We determine that Stern-Volmer quenching analysis is appropriate to extract rate constants for excited-state proton transfer in aqueous solutions from a weak photoacid, 5-aminonaphthalene-1-sulfonate, to a series of proton-accepting quenchers. Analysis of these data by Marcus-Cohen bond-energy-bond-order theory yields an accurate value for pKa* of 5-aminonaphthalene-1-sulfonate. Our method is broadly accessible because it only requires readily available steady-state photoluminescence spectroscopy. Moreover, our results for weak photoacids are consistent with those from previous studies of strong photoacids, each showing the applicability of kinetic theories to interpret driving-force-dependent rate constants for proton-transfer reactions.