We present a measurement of the cross section and transverse single-spin asymmetry (AN) for. mesons at large pseudorapidity from root s = 200 GeV p up arrow + p collisions. The measured cross section for 0.5 < p(T) < 5.0 GeV/c and 3.0 < vertical bar eta vertical bar < 3.8 is well described by a next-to-leading-order perturbative-quantum-chromodynamics calculation. The asymmetries A(N) have been measured as a function of Feynman-x (x(F)) from 0.2 < vertical bar x(F)vertical bar < 0.7, as well as transverse momentum (p(T)) from 1.0 < p(T) < 4.5 GeV/c. The asymmetry averaged over positive x(F) is < A(N)> = 0.061 +/- 0.014. The results are consistent with prior transverse single-spin measurements of forward eta and pi(0) mesons at various energies in overlapping x(F) ranges. Comparison of different particle species can help to determine the origin of the large observed asymmetries in p up arrow + p collisions.