The optical-optical double resonance (OODR) spectra of Rydberg (3) Sigma(+) states of Hg(n(3)S(1))Ne (n=8-10) and Hg(8(3)S(1))Ar were measured by using A and B states as intermediate states in the OODR process. The interatomic potentials of three states of HgNe and one state of HgAr were determined over a wide range of interatomic distance, R=3-7 Angstrom, by the analysis of the vibrational structure of their OODR spectra. It was found that the potential shape varies sensitively with n and converges to that of the ion core, HgNe+. Dissociation energies (D-e) of the Rydberg states for the n=8, 9, and 10 were derived to be 209(2), 284(2), and 309(2) cm(-1), respectively. Using the quantum defect orbital [G. Simons, J. Chem. Phys. 60, 645 (1974)], which represents a hydrogenic radial wave function for a Rydberg state with a given quantum defect, was introduced to interpret the characteristic n dependence of the interatomic potential. It was shown that the interatomic potential for the Rydberg states can be expressed by the sum of the ion core potential, V-ion(R), and the repulsive potential, V-ex(R), which originates mainly from the exchange repulsion between the Rydberg electron and the attached rare gas atom. The interatomic potential for Hg(8(3)S(1))Ar, whose dissociation energy [D-e=1602(4) cm(-1)] is much deeper than that of Hg(8(3)S(1))Ne, was also interpreted consistently by expressing the potential as V-ion(R) + V-ex(R).