We present detailed investigations of our previously reported observations of the 3(1)Delta(g) and 4(1)Delta(g) Rydberg states having separated-atom limits of Na(3s) + Na(4d) and Na(3s) + Na(4f), respectively, of Na-2 using high-resolution cw optical-optical double resonance spectroscopic measurements and analyzing the assigned rovibrational energy levels both by the individual linear fit method and the Dunham polynomial fit method. We have sorted out e/f-parity observed energy levels, and then from the Dunham polynomial fits of the e-parity levels, we have derived molecular constants and constructed Rydberg-Klein-Rees potentials of the 3(1)Delta(g) and 4(1)Delta(g) states, which appear to be twin states with an avoided crossing at R-c = 4.10 angstrom and a splitting of Delta E-c = 94 cm(-1). The potentials are in good agreement with the ab initio calculations and linear fit results. The Lambda-doubling splittings and the (f-d) l-mixing are investigated. A detailed discussion is focused on the adiabatic interaction of the perturbed molecular wave functions/states causing mutual amplitude/intensity sharing giving rise to avoided crossing between the 3(1)Delta(g) and 4(1)Delta(g) states.