  Aharonov's weak value, which is a physical quantity obtainable by weak
measurement, admits amplification and hence is deemed to be useful for
precision measurement. We examine the significance of the amplification based
on the uncertainty of measurement, and show that the trade-offs among the three
(systematic, statistical and nonlinear) components of the uncertainty inherent
in the weak measurement will set an upper limit on the usable amplification.
Apart from the Gaussian state models employed for demonstration, our argument
is completely general; it is free from approximation and valid for arbitrary
observables $A$ and couplings $g$.
