  Let $L^1_\om(G)$ be a Beurling algebra on a locally compact abelian group
$G$. We look for general conditions on the weight which allows the vanishing of
continuous derivations of $L^1_\om(G)$. This leads us to introducing
vector-valued Beurling algebras and considering the translation of operators on
them. This is then used to connect the augmentation ideal to the behavior of
derivation space. We apply these results to give examples of various classes of
Beurling algebras which are weakly amenable, 2-weakly amenable or fail to be
even 2-weakly amenable.
