PHENIX measurements are presented for the cross section and double-helicity asymmetry (A(LL)) in inclusive pi(0) production at midrapidity from p + p collisions at root s = 510 GeV from data taken in 2012 and 2013 at the Relativistic Heavy Ion Collider. The next-to-leading-order perturbative-quantum-chromodynamics theory calculation is in excellent agreement with the presented cross section results. The calculation utilized parton-to-pion fragmentation functions from the recent DSS14 global analysis, which prefer a smaller gluon-to-pion fragmentation function. The pi(0)A(LL) results follow an increasingly positive asymmetry trend with p(T) and root s with respect to the predictions and are in excellent agreement with the latest global analysis results. This analysis incorporated earlier results on pi(0) and jet A(LL) and suggested a positive contribution of gluon polarization to the spin of the proton Delta G for the gluon momentum fraction range x > 0.05. The data presented here extend to a currently unexplored region, down to x similar to 0.01, and thus provide additional constraints on the value of Delta G.