  A "weight" on a quiver $Q$ with values in a group $G$ is a function which
assigns an element of $G$ for each arrow in $Q$. This paper shows that the
essential steps in the mutation of quivers with potential [DWZ] goes through
with weights provided that the weights on each cycle in the potential have
trivial product. This gives another proof of the sign coherence of $c$-vectors.
We also classify all weights on tame quivers.
