  Several recent studies show that bright, intermediate and high redshift
optically and radio selected QSOs are positively correlated with nearby
galaxies on a range of angular scales up to a degree. Obscuration by unevenly
distributed Galactic dust can be ruled out as the cause, leaving weak
statistical lensing as the physical process responsible. However the amplitude
of correlations on < 1 degree scales is at least a factor of a few larger than
lensing model predictions. A possible way to reconcile the observations and
theory is to revise the weak lensing formalism. We extend the standard lensing
formulation to include the next higher order term (second order) in the
geodesic equation of motion for photons. We derive relevant equations
applicable in the weak lensing regime, and discuss qualitative properties of
the updated formulation. We then perform numerical integrations of the revised
equation and study the effect of the extra term using two different types of
cosmic mass density fluctuations. We find that nearby large-scale coherent
structures increase the amplitude of the predicted lensing-induced correlations
between QSOs and foreground galaxies by ~ 10% (not a factor of several required
by observations), while the redshift of the optimal, i.e. `most correlated'
structures is moved closer to the observer compared to what is predicted using
the standard lensing equation.
