  (Abridged) We investigate and quantify the impact of finite simulation volume
on weak lensing two- and four-point statistics. These {\it finite support} (FS)
effects are modelled for several estimators, simulation box sizes and source
redshifts, and validated against a new large suite of 500 $N$-body simulations.
The comparison reveals that our theoretical model is accurate to better than 5
per cent for the shear correlation function $\xi_{+}(\theta)$ and its error. We
find that the most important quantities for FS modelling is the ratio between
the measured angle $\theta$ and the angular size of the simulation box at the
source redshift, $\theta_{box}(z_s)$, or the multipole equivalent $\ell /
\ell_{box}(z_s)$. When this ratio reaches 0.1, independently of the source
redshift, the shear correlation function $\xi_+$ is suppressed by 5, 10, 20 and
25 percent for $L_{box}= 1000$, $500$, $250$ and $147\mbox{Mpc}/h$
respectively. When it reaches 0.2, the suppression exceeds 25 percent even for
the largest box. The same effect is observed in $\xi_{-}(\theta)$, but at much
larger angles. This has important consequences for cosmological analyses using
$N$-body simulations to calibrate the impact of non-linear gravitational
clustering or to estimate errors and systematics effects, and should not be
overlooked. We propose simple semi-analytic solutions to correct for these
finite box effects with and without the presence of survey masks, and the
method can be generalized to any weak lensing estimator. This offers a graceful
solution to the important problem of estimating accurate covariance matrices
for weak lensing studies: there is no need to run extra large simulation
volumes, as long as the box effects are corrected.
