  Motivated by searches for $0\nu\beta\beta$ decay in nuclear experiments and
collider probes of lepton number violation at dimension $d\geq7$, we
investigate the sensitivity to the $d=5$ Weinberg operator using the
non-resonant signature $pp\to \ell^\pm \ell'^{\pm} j j$ at the LHC. We develop
a prescription for the operator that is applicable in collisions and decays,
and focus on the $\ell\ell'=\mu\mu$ channel, which is beyond the reach of
nuclear decays. For a Wilson coefficient $C^{\mu\mu}_5=1$, scales as heavy as
$\Lambda\sim 8.3~(11)$~TeV can be probed with $\mathcal{L}=300~{\rm
fb}^{-1}~(3~{\rm ab}^{-1})$. This translates to an effective $\mu\mu$ Majorana
mass of $\vert m_{\mu\mu}\vert\sim7.3~(5.4)$~GeV, and establishes a road map
for testing the Weinberg operator at accelerators.
