  Recently, weak value $\rm A_w$ derived in the pre- and post-selected weak
measurement has been shown to be powerful in measuring minute physical effects.
In principle, the decrease in the post-selection probability will increase the
sensitivity. Besides, the sensitivity which characterizes the pointer position
shift is proportional to the real part of $\rm A_w$, and the sensitivity which
characterizes the pointer shift in momentum space is proportional to the
imaginary part of $\rm A_w$. However, we find that the relationship between the
post-selection probability and the sensitivity is true when $\rm A_w$ is a
purely real number or a purely imaginary number. The plural $\rm A_w$ will lead
to the abnormal behavior where the decrease in the post-selection probability
reduce the sensitivity at certain pre- and post-selection. In addition,
considering the device imperfections and the environmental instability in the
WVA protocol, this anomaly raised from plural $\rm A_w$ will reduce the
sensitivity and generate a systematic error of the measurement compared with
the original scheme. Finally, three feasible methods are proposed to reduce
these negative effects when the weak measurement inevitably changes into
measurement with a plural weak value.
