  In recent years a number of correlation measurements in nuclear $\beta$ decay
have been performed reaching a precision of the order of 1\% and below and it
is expected that even higher precision will be reached in the near future. At
these levels of precision higher-order corrections due to e.g. recoil terms
induced by the strong interaction and radiative corrections cannot necessarily
be neglected anymore when interpreting these results in terms of new physics or
extracting a value for the $V_{ud}$ quark-mixing matrix element. We provide
here an update of the $\mathcal{F} t$ values of the $T=1/2$ mirror $\beta$
decays as well as an overview of current experimental and theoretical knowledge
of the most important recoil term, weak magnetism, for both the $T=1/2$ mirror
$\beta$ transitions and a large set of $\beta$ decays in higher isospin
multiplets. The matrix elements determining weak magnetism were calculated in
the nuclear shell model and cross-checked against experimental data, showing
overall good agreement. Additionally, we show that further insight can be
obtained from properly deformed nuclear potentials, in particular for mirror
$T=1/2$ decays.. The results provide new insights in the size of weak
magnetism, extending the available information to $\beta$ transitions of nuclei
with masses up to $A =$ 75. This provides important guidance for the planning
and interpretation of ongoing and new precise correlation measurements in
nuclear $\beta$ decay searching for new physics or to extract the $V_{ud}$
quark-mixing matrix element in mirror $\beta$ decays. This more detailed
knowledge of weak magnetism can also be of interest for further theoretical
work related to the reactor neutrino problem.
