  D. G. Higman generalized a coherent configuration and defined a weight. In
this article, we will modify the definition and investigate weights on coherent
configurations. If our weights are on a thin homogeneous coherent
configuration, that is essentially a finite group, then there is a natural
correspondence between the set of equivalence classes of weights and
$2$-cohomology group of the group. We also give a construction of weights as a
generalization of Higman's method using monomial representations of finite
groups.
