  The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation
symmetries, is a fundamental model for investigating quantum matters with
topology and correlations. With the rise of the moir\'e-based design of model
systems, realizing a tunable and symmetric honeycomb lattice system with a
narrow bandwidth can open access to new phases and insights. We propose the
ABBA-stacked twisted double bilayer WSe$_2$ as a realistic and tunable platform
for reaching this goal. Adjusting the twist angle allows the bandwidth and the
ratio between hopping parameters of different ranges to be tuned. Moreover, the
system's small bandwidth and spin rotation symmetry enable effective control of
the electronic structure through an in-plane magnetic field. We construct an
extended Hubbard model for the system to demonstrate this tunability and
explore possible ordered phases using the Hartree-Fock approximation. We find
that at a hole filling of $\nu = 2$ (two holes per moir\'e unit cell), an
in-plane magnetic field of a few Tesla can ``dope" the system from a semimetal
to a metal. Interactions then drive an instability towards a canted
antiferromagnetic insulator ground state. Additionally, we observe a competing
insulating phase with sublattice charge polarization. Finally, we discuss the
experimental signatures of these novel insulating phases.
