Weyl semimetals are predicted to host signature magneto-optical properties sourced by their peculiar Landau-level structure, including the chiral level. Analytical studies are often leaving out the Hall component of the conductivity due to its complicated nature, and even though the chiral anomaly requires Weyl nodes to come in charge-conjugate pairs, toy models hosting only one node are considered almost exclusively; numerical studies including several Weyl nodes are, on the other hand, often limited to high-field quantum limits or dc studies. Here, we present a twofold purpose study, where we (a) analytically derive a closed-form expression also for the Hall conductivity of a generic Weyl semimetal using linear response theory and (b) apply this general framework to evaluate the transverse conductivity components for Weyl systems with two nodes. We study how various model parameters, including the tilt, momentum separation, and energy location of the nodes, as well as the chemical potential, affect the magneto-optical conductivity, and complement these studies by deriving an analytical expression for the dc Hall conductivity, which is also evaluated in various systems. Including a chiral pair of nodes results in two important differences compared to earlier studies: the contribution from the chiral level is equal in size but opposite at the two nodes, making the net contribution disappear, and the energy scales at which intraband transitions occur is smeared out and approaches that of interband transitions, strengthening the hypothesis that intraband transitions mask signature optical features in materials. This general formalism can be applied to a large family of generic Weyl semimetals, and comprise an important piece towards unravelling the source of the mismatch between theoretical predictions and experimental observations in candidate materials.