  Upcoming deep imaging surveys such as the Vera C. Rubin Observatory Legacy
Survey of Space and Time will be confronted with challenges that come with
increased depth. One of the leading systematic errors in deep surveys is the
blending of objects due to higher surface density in the more crowded images; a
considerable fraction of the galaxies which we hope to use for cosmology
analyses will overlap each other on the observed sky. In order to investigate
these challenges, we emulate blending in a mock catalogue consisting of
galaxies at a depth equivalent to 1.3 yr of the full 10-yr Rubin Observatory
that includes effects due to weak lensing, ground-based seeing, and the
uncertainties due to extraction of catalogues from imaging data. The emulated
catalogue indicates that approximately 12 per cent of the observed galaxies are
``unrecognized'' blends that contain two or more objects but are detected as
one. Using the positions and shears of half a billion distant galaxies, we
compute shear--shear correlation functions after selecting tomographic samples
in terms of both spectroscopic and photometric redshift bins. We examine the
sensitivity of the cosmological parameter estimation to unrecognized blending
employing both jackknife and analytical Gaussian covariance estimators. An
$\sim0.025$ decrease in the derived structure growth parameter $S_8 = \sigma_8
(\Omega_{\rm m}/0.3)^{0.5}$ is seen due to unrecognized blending in both
tomographies with a slight additional bias for the photo-$z$-based tomography.
This bias is greater than the $2\sigma$ statistical error in measuring $S_8$.
