Proton activity in electrolytes plays a crucial role in deciding the electrochemical performance of aqueous batteries. On the one hand, it can influence the capacity and rate performance of host materials because of the high redox activity of protons. On the other hand, it can also cause a severe hydrogen evolution reaction (HER) when the protons are aggregated near the electrode/electrolyte interface. The HER dramatically limits the potential window and the cycling stability of the electrodes. Therefore, it is critical to clarify the impact of electrolyte proton activity on the battery macro-electrochemical performance. In this work, using an aza-based covalent organic framework (COF) as a representative host material, we studied the effect of electrolyte proton activity on the potential window, storage capacity, rate performance, and cycle stability in various electrolytes. A tradeoff relationship between proton redox reactions and the HER in the COF host is revealed by utilizing various in situ and ex situ characterizations. Moreover, the origin of proton activity in near-neutral electrolytes is discussed in detail and is confirmed to be related to the hydrated water molecules in the first solvation shell. A detailed analysis of the charge storage process in the COFs is presented. These understandings can be of importance for utilizing the electrolyte proton activity to build high-energy aqueous batteries.