  JWST has revealed a population of low-luminosity AGN at $z>4$ in compact, red
hosts (the "Little Red Dots", or LRDs), which are largely undetected in X-rays.
We investigate this phenomenon using GRRMHD simulations of super-Eddington
accretion onto a SMBH with $M_\bullet=10^7 \,\rm M_\odot$ at $z\sim6$,
representing the median population; the SEDs that we obtain are intrinsically
X-ray weak. The highest levels of X-ray weakness occur in SMBHs accreting at
mildly super-Eddington rates ($1.4<f_{\rm Edd}<4$) with zero spin, viewed at
angles $>30^\circ$ from the pole. X-ray bolometric corrections in the observed
$2-10$ keV band reach $\sim10^4$ at $z=6$, $\sim5$ times higher than the
highest constraint from X-ray stacking. Most SEDs exhibit $\alpha_{\rm ox}$
values outside standard ranges, with X-ray weakness increasing with optical-UV
luminosity; they are also extraordinarily steep and soft in the X-rays (median
photon index $\Gamma=3.1$, mode of $\Gamma=4.4$). SEDs strong in the X-rays
have harder spectra with a high-energy bump when viewed near the hot ($>10^8$
K) and highly-relativistic jet, whereas X-ray weak SEDs lack this feature.
Viewing a SMBH within $10^\circ$ of its pole, where beaming enhances the X-ray
emission, has a $\sim1.5\%$ probability, matching the LRD X-ray detection rate.
Next-generation observatories like AXIS will detect X-ray weak LRDs at $z\sim6$
from any viewing angle. Although many SMBHs in the LRDs are already estimated
to accrete at super-Eddington rates, our model explains $50\%$ of their
population by requiring that their masses are overestimated by a mere factor of
$\sim3$. In summary, we suggest that LRDs host slowly spinning SMBHs accreting
at mildly super-Eddington rates, with large covering factors and broad emission
lines enhanced by strong winds, providing a self-consistent explanation for
their X-ray weakness and complementing other models.
