We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with weak interlayer versus intralayer exchange coupling have strong magnetoelectric response that can be detected in dual-gated devices where internal displacement fields and carrier densities can be varied independently. We illustrate this strong temperature-dependent magnetoelectric response in bilayer CrI3 at charge neutrality by calculating the gate voltage-dependent total magnetization through Monte Carlo simulations and mean-field solutions of the anisotropic Heisenberg model informed from density functional theory and experimental data and present a simple model for electrical control of magnetism by electrostatic doping.