  Moir\'e materials with flat electronic bands provide a highly controllable
quantum system for studies of strong-correlation physics and topology. In
particular, angle-aligned heterobilayers of semiconducting transition metal
dichalcogenides (TMDs) with large band offset realize the single-band Hubbard
models. Introduction of a new layer degree of freedom is expected to foster
richer interactions, enabling Hund's physics, interlayer exciton condensation
and new superconducting pairing mechanisms to name a few. Here, we report
competing electronic orders in twisted AB-homobilayer WSe2, which realizes a
bilayer Hubbard model in the weak interlayer hopping limit for holes. We
characterize the charge order, layer polarization and magnetization of the
moir\'e bilayer, subjected to an out-of-plane electric and magnetic field, by
exciton sensing and magneto circular dichroism measurements. By
layer-polarizing holes via the electric field, we observe a crossover from an
excitonic insulator to a charge-transfer insulator at hole density of $\nu$=1
(in unit of moir\'e density), a transition from a paramagnetic to an
antiferromagnetic charge-transfer insulator at $\nu$=2, and evidence for a
layer-selective Mott insulator at 1<$\nu$<2. The unique coupling of charge and
spin to external fields also manifests a giant magneto-electric response. Our
results establish a new solid-state simulator for problems in
strong-correlation physics that are described by bilayer Hubbard models.
