The aim of this work is to construct families of weighing matrices via their
automorphism group action. This action is determined from the
0,1,2-cohomology groups of the underlying abstract group. As a consequence,
some old and new families of weighing matrices are constructed. These include
the Paley Conference, the Projective-Space, the Grassmannian, and the
Flag-Variety weighing matrices. We develop a general theory relying on low
dimensional group-cohomology for constructing automorphism group actions, and
in turn obtain structured matrices that we call \emph{Cohomology-Developed
matrices}. This "Cohomology-Development" generalizes the Cocyclic and Group
Developments. The Algebraic structure of modules of Cohomology-Developed
matrices is discussed, and an orthogonality result is deduced. We also use this
algebraic structure to define the notion of \emph{Quasiproducts}, which is a
generalization of the Kronecker-product