We report new STAR measurements of the single-spin asymmetries A(L) for W+ and W- bosons produced in polarized proton-proton collisions at root 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) over bar and (b) over bar quark helicity distributions for 0.05 < x < 0.25. In addition, we report new results for the double-spin asymmetries A(LL) for W-+/-, as well as A(L) for Z/gamma* production and subsequent decay into electron-positron pairs.