We report new STAR measurements of the single-spin asymmetries AL for W+ and W- bosons produced in polarized proton-proton collisions at s=510 GeV as a function of the decay-positron and decay-electron pseudorapidity. The data were obtained in 2013 and correspond to an integrated luminosity of 250 pb-1. The results are combined with previous results obtained with 86 pb-1. A comparison with theoretical expectations based on polarized lepton-nucleon deep-inelastic scattering and prior polarized proton-proton data suggests a difference between the u ̄ and d ̄ quark helicity distributions for 0.05<x<0.25. In addition, we report new results for the double-spin asymmetries ALL for W±, as well as AL for Z/γ* production and subsequent decay into electron-positron pairs.