  In the weak measurement (WM) scenario involving weak interaction and
postselection by projective measurement, the empirical significance of weak
values is manifested in terms of shifts in the measurement pointer's mean
position and mean momentum. In this context, a general quantitative treatment
is presented in this paper by taking into account the hitherto unexplored
effect of correlations among the pointer degrees of freedom which pertain to an
arbitrary multidimensional preselected pointer state. This leads to an
extension of the earlier results, showing that, for complex weak values, the
correlations among different pointer degrees of freedom can crucially affect
the way the imaginary parts of the weak values are related to the observed
shifts of the mean pointer position and momentum. The particular relevance of
this analysis is discussed in the case of sequential weak interactions,
followed by a postselection (called sequential WM) which, in the special case,
reduces to the usual WM scheme involving a single weak interaction and
postseletion, modified by the effect of pointer state correlations.
