Convolutional codes can be described by linear input-state-output systems. This gives rise to a state transition graph and an associated weight adjacency matrix. The latter counts in a detailed way the weights occurring in the code. After discussing some uniqueness issues we will present a MacWilliams identity theorem for convolutional codes and their duals in terms of the weight adjacency matrix. Furthermore, we will discuss isometries for convolutional codes and their effect on the weight adjacency matrix. It will be shown that for a particular class of codes the weight adjacency matrix forms a complete invariant under monomial equivalence, that is, under permutation and rescaling of the codeword coordinates.