We theoretically study the electromagnetic response of type-I and type-II centrosymmetric Weyl metals. We derive an anisotropic permittivity tensor with off-diagonal elements to describe such gyrotropic media. Our findings reveal that for appropriate Weyl cones tilts, the real part of the transverse component of the permittivity can exhibit an ϵ-near-zero response. The tilt parameter can also control the amount of loss in the medium, ranging from lossless to dissipative when transitioning from type-I to type-II. Similarly, by tuning either the frequency of the electromagnetic field or the chemical potential in the system, an ϵ-near-zero response can appear as the permittivity of the Weyl semimetal transitions between positive and negative values. Employing the obtained permittivity tensor, we consider a setup where the Weyl semimetal is deposited on a perfect conductive substrate and study the refection and absorption characteristics of this nano-layered configuration. We show that by choosing the proper geometrical and material parameters, devices can be created that perfectly absorb electromagnetic energy over a wide angular range of incident electromagnetic waves.