Relativistic effects on the Xe129 nuclear magnetic resonance shielding and Xe131 nuclear quadrupole coupling (NQC) tensors are examined in the weakly bound Xe2 system at different levels of theory including the relativistic four-component Dirac-Hartree-Fock (DHF) method. The intermolecular interaction-induced binary chemical shift δ, the anisotropy of the shielding tensor Δσ, and the NQC constant along the internuclear axis χ‖ are calculated as a function of the internuclear distance. DHF shielding calculations are carried out using gauge-including atomic orbitals. For comparison, the full leading-order one-electron Breit-Pauli perturbation theory (BPPT) is applied using a common gauge origin. Electron correlation effects are studied at the nonrelativistic (NR) coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level of theory. The fully relativistic second-order Møller-Plesset many-body perturbation (DMP2) theory is used to examine the cross coupling between correlation and relativity on NQC. The same is investigated for δ and Δσ by BPPT with a density functional theory model. A semiquantitative agreement between the BPPT and DHF binary property curves is obtained for δ and Δσ in Xe2. For these properties, the currently most complete theoretical description is obtained by a piecewise approximation where the uncorrelated relativistic DHF results obtained close to the basis-set limit are corrected, on the one hand, for NR correlation effects and, on the other hand, for the BPPT-based cross coupling of relativity and correlation. For χ‖, the fully relativistic DMP2 results obtain a correction for NR correlation effects beyond MP2. The computed temperature dependence of the second virial coefficient of the Xe129 nuclear shielding is compared to experiment in Xe gas. Our best results, obtained with the piecewise approximation for the binary chemical shift combined with the previously published state of the art theoretical potential energy curve for Xe2, are in excellent agreement with the experiment for the first time.