The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation symmetries, is a fundamental model for investigating quantum matter with topology and correlations. With the rise of the moiré-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 WSe2 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 ν=2 (two holes per moiré 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 insulating phases. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.