Carbon nanotubes are one-dimensional nanoscale systems with strongly pronounced chirality-dependent optical properties with multiple excitonic transitions. We investigate the high-energy G mode of semiconducting single-walled nanotubes of different chiralities at first excitonic transition by applying resonant Raman spectroscopy. The G mode intensity dependence on excitation energy yielded asymmetric resonance Raman profiles similar to ones we reported for the second excitonic transition. We find the scattering efficiency to be strongest at the incoming Raman resonance. Still, the degree of asymmetry is different for the first and second transitions and the first transition profiles provide a narrower line shape due to longer exciton lifetimes. The overall scattering efficiency is up to a factor of 25 times more intense at first excitonic transition, compared to the second transition. The fifth-order perturbation theory, with implemented phonon scattering pathways between excitonic states, excellently reproduced experimental data.