Mr. Collins is fixated with Lady Catherine.
His obsession with her is revealed in both his words and actions.
His must constantly remind people of his connection with her and therefore
his perceived higher place in society. This is evident, for instance,
when he presumes to make Darcy's acquaintance on the premise that Darcy
is Lady Catherine's nephew and thus must be someone worth knowing.
He also has a compulsion to speak
of Lady Catherine whenever possible and is quick to insert her name into
any conversation whether it is about his marriage, career, or even the
design of his house. In fact, most of his decisions are motivated
as an attempt to please her. Even his proposal to Elizabeth includes
the explanation that it has been suggested by Lady Catherine that he should
marry.
Further example of his obsession is
his near stalking of Lady Catherine, for instance when Charlotte admits
to Elizabeth that Mr. Collins will often sit by the window for hours at
a time waiting for a glimpse of Lady Catherine's carriage.