  Whilst the underlying assumption of the Friedman-Lema\^itre-Robertson-Walker
(FLRW) cosmological model is that matter is homogeneously distributed
throughout the universe, gravitational influences over the life of the universe
have resulted in mass clustered on a range of scales. Hence we expect that, in
our inhomogeneous universe, the view of an observer will be influenced by the
location and local environment. Here we analyse the one-point probability
distribution functions and angular power spectra of weak-lensing (WL)
convergence and magnification numerically to investigate the influence of our
local environment on WL statistics in relativistic $N$-body simulations. To
achieve this, we numerically solve the null geodesic equations which describe
the propagation of light bundles backwards in time from today, and develop a
ray-tracing algorithm, and from these calculate various WL properties. Our
findings demonstrate how cosmological observations of large-scale structure
through WL can be impacted by the locality of the observer. We also calculate
the constraints on the cosmological parameters as a function of redshift from
the theoretical and numerical study of the angular power spectrum of WL
convergence. This study concludes the minimal redshift for the constraint on
the parameter $\Omega_m$ ($H_0$) is $z \sim 0.2$ $(z \sim 0.6 )$ beyond which
the local environment's effect is negligible and the data from WL surveys are
more meaningful above that redshift. The outcomes of this study will have
direct consequences for future surveys, where percent-level-precision is
necessary.
