We have spectroscopically investigated the thermally and doping-induced metal-insulator transitions for pyrochlore-type Nd2Ir2O7 as well as its Rh-doped analogs Nd2(Ir(1-x)Rh(x))(2)O(7), where the spin-orbit interaction as well as the electron correlation is effectively tuned by the doping level (x). The charge dynamics dramatically changes on an energy scale of 1 eV in the course of thermally and doping-induced metal-insulator transitions, while the insulating ground state shows a small but well-defined charge gap of 45 meV. Anomalous doping variation of the low-energy (<0.3 eV) optical-conductivity spectra at the ground state can be interpreted in terms of the phase changes among the narrow-gap Mott insulator, Weyl semimetal, and correlated metal.