  We interpret the 2 TeV excesses at the LHC in a left-right symmetric model
with Higgs doublets and spontaneous $D$-parity violation. The light neutrino
masses are understood via a linear seesaw, suppressed by a high $D$-parity
breaking scale, and the heavy neutrinos have a pseudo-Dirac character. In
addition, with a suppressed right-handed gauge coupling $g_R / g_L \approx 0.6$
in an $SO(10)$ embedding, we can thereby interpret the observed $eejj$ excess
at CMS. We show that it can be reconciled with the diboson and dijet excesses
within a simplified scenario based on our model. Moreover, we find that the
mixing between the light and heavy neutrinos can be potentially large which
would induce dominant non-standard contributions to neutrinoless double beta
decay via long-range $\lambda$ and $\eta$ neutrino exchange.
