  Inspired by a string duality, we construct a deformation family for
$G_2$-orbifolds given as total spaces of coassociative fibrations by ADE
singularities over a closed and oriented smooth three-manifold $Q$. The
deformations are parametrized by sections of a fiber bundle on $Q$ that can be
interpreted as spectral/cameral covers associated to certain Riemannian analogs
of Higgs bundles. The spectral cover picture is a unifying framework for
several different approaches to coassociative fibrations appearing in the
literature. Our construction generalizes, to the context of $G_2$-geometry, a
well-known family of ADE-fibered Calabi-Yau threefolds whose deformations are
parametrized by spectral covers of holomorphic Higgs bundles on its base
Riemann surface.
