  It is shown that the right shift semigroup on $L^2(\mathbb{R}_+)$ does not
satisfy the weighted Weiss conjecture for $\alpha \in (0,1)$. In other words,
$\alpha$-admissibility of scalar valued observation operators cannot always be
characterised by a simple resolvent growth condition. This result is in
contrast to the unweighted case, where 0-admissibility can be characterised by
a simple growth bound. The result is proved by providing a link between
discrete and continuous $\alpha$-admissibility and then translating a
counterexample for the unilateral shift on $H^2(\mathbb{D})$ to continuous time
systems.
