Polymers have been used as additives in the liquid electrolytes typically used for secondary batteries that utilize metals as anode. Such additives are conventionally argued to improve long-term anode performance by suppressing morphological and hydrodynamic instabilities thought to be responsible for out-of-plane and dendritic metal deposition during battery charging. More recent studies have reported that the polymer additives provide even more fundamental mechanisms for stabilizing metal electrodeposition through their ability to regulate metal electrodeposit crystallography and, thereby, morphology. Few studies explore how polymers carried in a liquid electrolyte achieve these functions, and fewer still provide rules for choosing among the various polymer types, the additive polymer molecular weight (Mw), and concentration in the electrolyte. Here, we investigate how these generally easy-to-control variables influence electrochemical interphase formation inside battery cells and their impact on the morphology and reversibility of Zn electrodes in aqueous electrolytes. We focus on aqueous Zn-iodine electrochemical cells containing linear polyethylene glycol (PEG) chains as additives and find that in electrolytes where the polymer concentration is maintained in the dilute solution regime there is an optimum polymer molecular weight (Mw ≈ 1000 Da), above which beneficial effects of polymers on Zn electrode reversibility and Zn-I2 battery lifetime are progressively lost. By means of optical ellipsometry and theoretical calculations, we show that the optimal Mw is associated with saturation of the thickness of a physiosorbed PEG coating on the Zn metal electrode. Electron microscopy and X-ray photoelectron spectroscopy analysis of Zn electrodeposits formed in such electrolytes reveal that the physiosorbed polymer coating has two primary effects─it regulates the deposit morphology and suppresses parasitic reactions between the electrode and electrolyte components. The parasitic reactions produce species like ZnO, which are known to passivate the Zn electrode and promote nonuniform deposition. Galvanostatic cycling measurements in aqueous Zn-I2 cells containing the PEG additives at the optimal Mw show that the cells maintain very high Coulombic efficiencies (≥99%) at current densities as high as 50 mA/cm2─close to the maximum values permissible across the Celgard separator membranes used in our studies.