The Extension Theorem states that, for a given weight on he alphabet, every linear isometry between linear codes extends to a mono- mial transformation of the entire space. This theorem has been proved for several weights and alphabets, including the original MacWilliams' Equivalence Theorem for Hamming weight on codes over nite elds. Now we ask: What conditions must a weight satisfy so that the Extension Theorem will hold? In this paper we provide an algebraic framework for determining such conditions, generalising the approach taken in [5].