Nickelate superconductors provide a valuable new platform for the study of unconventional superconductivity that is complementary to the cuprates. One of the central puzzles about hightemperature superconductors is what factors determine the scale of their superconducting transition temperature (Tc). To address this question for infinite-layer nickelates, we present a systematic mutual inductance study of the superfluid density across the doping-dependent superconducting dome of Nd1−xSrxNiO2. We observe a weak superfluid stiffness that exhibits an approximately square-root correlation with Tc. We also find a strong interplay between Nd magnetism and the superconducting phase, manifested as a substantial low-temperature suppression of superfluid density. These observations highlight the importance of superconducting phase fluctuations in limiting Tc and pronounced coupling between the Nd 4f moments and the superfluid.