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TaAs and NbAs are two of the earliest identified Weyl semimetals that possess many intriguing optical properties, such as chirality-dependent optical excitations and giant second harmonic generation (SHG). Linear and nonlinear optics have been employed as tools to probe the Weyl physics in these crystals. Here we extend these studies to address two important points: determining the complete anisotropic dielectric response, and to explore if and how they can reveal essential Weyl physics. For the first time, we determine the complete anisotropic dielectric functions of TaAs and NbAs by combining spectroscopic ellipsometry and density functional theory (DFT). Parameterized Lorentz oscillators are reported from 1.2-6 eV (experiment) and 0-6 eV (DFT), and good agreement is shown between them. Both linear and nonlinear optical properties have been reported to reveal Weyl physics. We suggest that strong optical resonances from trivial bands are the likely origin of the large optical second harmonic generation previously reported at these energies. Furthermore, by comparing the contribution of a small k-space centered around the Weyl cones to the total linear dielectric function, we find that these contributions are highly anisotropic and are <25% of the total dielectric function below 0.5 eV; above 1eV, these contributions are negligible. Thus, the study of Weyl physics using optical techniques requires very low energies and even there, a careful assessment is required in distinguishing the much smaller contributions of the Weyl bands from the dominant contributions of the trivial bands and Drude response to the total dielectric function.