  We propose a scheme to enhance the fidelity of symmetric quantum cloning
machine using a weak measurement. By adjusting the intensity of weak
measurement parameter $p$, we obtain the copies with different optimal
fidelity. Choosing proper value of $p$, we can obtain the perfect copies for
initial qubits. In this paper, we focus on $1-2$ quantum cloning for two
nonorthogonal states. Sets containing more than two linear independent states
are also discussed briefly. Due to weak measurements being probabilistic, we
obtain high fidelity at risk of probability. If the weak measurement successes,
we do the following operations to obtain copies with high fidelity, otherwise,
the cloning process fails and we need do nothing. From this perspective, the
scheme we propose is economical for saving quantum resource and time, which may
be very useful in quantum information processing.
