We report the nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements for non-centrosymmetric superconductors Re7B3, LaBiPt, and BiPd containing heavy elements. For all three compounds, the spin-lattice relaxation rate 1/T-1 shows a coherence peak just below T-c and decreases exponentially at low temperatures, which indicates that an isotropic superconducting gap is dominant in these compounds. In BiPd, the height of the coherence peak just below T-c is much suppressed, which suggests that there exists a substantial component of gap with nodes in this compound. Our results indicate that heavy element is not the only factor, but the extent of inversion symmetry breaking is also important to induce a large spin-orbit coupling and an unconventional superconducting state.