BaMn2As2 is unique among BaT2As2 compounds crystallizing in the body-centered-tetragonal ThCr2Si2 structure, which contain stacked square lattices of 3d transition metal T atoms, since it has an insulating large-moment (3.9 µB/Mn) G-type (checkerboard) antiferromagnetic AF ground state. We report measurements of the anisotropic magnetic susceptibility χ versus temperature T from 300 to 1000 K of single crystals of BaMn2As2, and magnetic inelastic neutron scattering measurements at 8 K and 75 As NMR measurements from 4 to 300 K of polycrystalline samples. The Néel temperature determined from the χ(T ) measurements is TN = 618(3) K. The measurements are analyzed using the J1-J2-Jc Heisenberg model for the stacked square lattice, where J1 and J2 are respectively the nearest-neighbor (NN) and next-nearest-neighbor intraplane exchange interactions and Jc is the NN interplane interaction. Linear spin wave theory for G-type AF ordering and classical and quantum Monte Carlo simulations and molecular field theory calculations of χ(T ) and of the magnetic heat capacity Cmag(T ) are presented versus J1, J2 and Jc. We also obtain band theoretical estimates of the exchange couplings in BaMn2As2. From analyses of our χ(T ), NMR, neutron scattering, and previously published heat capacity data for BaMn2As2 on the basis of the above theories for the J1-J2-Jc Heisenberg model and our band-theoretical results, our best estimates of the exchange constants in BaMn2As2 are J1 ≈ 13 meV, J2/J1 ≈ 0.3 and Jc/J1 ≈ 0.1, which are all antiferromagnetic. From our classical Monte Carlo simulations of the G-type AF ordering transition, these exchange parameters predict TN ≈ 640 K for spin S = 5/2, in close agreement with experiment. Using spin wave theory, we also utilize these exchange constants to estimate the suppression of the ordered moment due to quantum fluctuations for comparison with the observed value and again obtain S = 5/2 for the Mn spin.