Giant anomalous Hall effect (AHE) and magneto-optical activity can emerge in magnets with topologically non-trivial degeneracies. However, identifying the specific band structure features like Weyl points, nodal lines or planes which generate the anomalous response is a challenging issue, requiring reliable spectroscopic techniques. Since the low-energy interband transitions can govern the static AHE, we address this question in the prototypical magnetic Weyl semimetal Co₃Sn₂S₂, also hosting nodal lines, by broadband polarized reflectivity and magneto-optical Kerr effect spectroscopy with a focus on the far-infrared range. In the optical Hall conductivity spectrum, we observe a strong resonance at 40 meV which primarily determines the static AHE, thus confirms its intrinsic origin. Our material-specific theory reproduces the experimental data remarkably well and shows that the nodal lines gapped by spin-orbit coupling around the Fermi energy generate large hotspots of Hall spectral weight. In addition, we verify that the tilt of the nodal line is a crucial factor which can produce a nodal line resonance. While the Weyl points only give vanishing contributions, these segments of the nodal lines dominate the low-energy magneto-optical response. Remarkably, we find that the linear dichroism for in- vs. out-of-plane directions is significantly enhanced by the nodal line resonance, leading to a potentially new signature of topological states. Interestingly, applying an in-plane magnetic field alters the optical signatures of the gapped nodal line, suggesting a band reconstruction coupled to the magnetisation direction.