  Residuals between measured galactic radii and those predicted by the
Fundamental Plane (FP) are possible tracers of weak lensing magnification.
However, observations have shown these to be systematically correlated with the
large-scale structure. We use the Horizon-AGN hydrodynamical cosmological
simulation to analyse these intrinsic size correlations (ISCs) for both
elliptical (early-type) and spiral (late-type) galaxies at $z=0.06$. We fit
separate FPs to each sample, finding similarly distributed radius residuals,
$\lambda$, in each case. We find persistent $\lambda\lambda$ correlations over
three-dimensional separations $0.5-17\,h^{-1}{\rm{Mpc}}$ in the case of spiral
galaxies, at $>3\sigma$ significance. When relaxing a mass-selection, applied
for better agreement with galaxy clustering constraints, the spiral
$\lambda\lambda$ detection strengthens to $9\sigma$; we detect a $5\sigma$
density-$\lambda$ correlation; and we observe intrinsically-large spirals to
cluster more strongly than small spirals over scales
$\lesssim10\,h^{-1}{\rm{Mpc}}$, at $>5\sigma$ significance. Conversely, and in
agreement with the literature, we observe lower-mass, intrinsically-small
ellipticals to cluster more strongly than their large counterparts over scales
$0.5-17\,h^{-1}{\rm{Mpc}}$, at $>5\sigma$ significance. We model
$\lambda\lambda$ correlations using a phenomenological non-linear size model,
and predict the level of contamination for cosmic convergence analyses. We find
the systematic contribution to be of similar order to, or dominant over the
cosmological signal. We make a mock measurement of an intrinsic, systematic
contribution to the projected surface mass density $\Sigma(r)$ and find
statistically significant, low-amplitude, positive (negative) contributions
from lower-mass spirals (ellipticals), which may be of concern for large-scale
($\gtrsim\,7\,h^{-1}$ Mpc) measurements.
