  We theoretically study the interplay between magnetism and a heavy Fermi
liquid in the AB stacked transition metal dichalcogenide bilayer system
MoTe$_2$/WSe$_2$ in the regime in which the Mo layer supports localized
magnetic moments coupled by interlayer electron tunnelling to a weakly
correlated band of itinerant electrons in the W layer. We show that the
interlayer electron transfer leads to a chiral Kondo exchange, with
consequences including a strong dependence of the Kondo temperature on carrier
concentration, a topological hybridization gap and an anomalous Hall effect.
The theoretical model exhibits two phases, a small Fermi surface magnet and a
large Fermi surface heavy Fermi liquid; the transition between them is first
order. A low-energy theory is developed for the the transport properties of the
two states. Implications of our results for present and future experiments on
MoTe$_2$/WSe$_2$ bilayer heterostructures are discussed.
