= Solution
Integrate <Poisson equation for Newtonian gravity> through a narrow slab around the disk. The horizontal derivative contributions vanish as its thickness tends to zero, leaving the normal-derivative jump
$$
\partial_z\Phi(0^+)-\partial_z\Phi(0^-)=4\pi G\Sigma.
$$
The <even function> symmetry of $\Phi$ makes the derivatives opposite, so
$$
\boxed{\partial_z\Phi(0^+)=2\pi G\Sigma.}
$$
In the current-free simply connected upper half-space, <Ampère's circuital law> gives $\nabla\times\mathbf B=0$ and permits a <magnetic scalar potential>. Rescale it so that $\sqrt{4\pi G/\mu_0}\,\mathbf B=-\nabla\Phi_M$. The <divergence>-free condition makes $\Phi_M$ satisfy <Laplace's equation>, with
$$
\partial_z\Phi_M(0^+)=-\sqrt{\frac{4\pi G}{\mu_0}}B_{z0}.
$$
Compare with the gravitational jump condition. Subject to the same isolated-field boundary condition at infinity, $\Phi_M$ is the harmonic potential of the effective <surface density>
$$
\boxed{\Sigma_M=-\frac{B_{z0}}{\sqrt{\pi G\mu_0}}.}
$$
This <gravity-equivalent magnetic surface density> can have either sign; it is a mathematical representation of the exterior <magnetic field>, not physical negative mass. An imposed nondecaying field would require additional boundary data and would not be fixed by the disk <surface density> alone.
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