  We show that the core of a weakly group-theoretical braided fusion category
$\C$ is equivalent as a braided fusion category to a tensor product $\B
\boxtimes \D$, where $\D$ is a pointed weakly anisotropic braided fusion
category, and $\B \cong \vect$ or $\B$ is an Ising braided category. In
particular, if $\C$ is integral, then its core is a pointed weakly anisotropic
braided fusion category. As an application we give a characterization of the
solvability of a weakly group-theoretical braided fusion category. We also
prove that an integral modular category all of whose simple objects have
Frobenius-Perron dimension at most 2 is necessarily group-theoretical.
