  We introduce and study the "kicked Hall system" (KHS), i.e., charged
particles periodically kicked in the presence of uniform magnetic
($\mathbf{B}$) and electric ($\mathbf{E}$) fields that are perpendicular to
each other and to the kicking direction. We show that for resonant values of
$B$ and $E$ and in the weak-chaos regime of sufficiently small nonintegrability
parameter $\kappa$ (the kicking strength), there exists a \emph{generic} family
of periodic kicking potentials for which the Hall effect from $\mathbf{B}$ and
$\mathbf{E}$ significantly suppresses the weak chaos, replacing it by
\emph{"superweak"} chaos (SWC). This means that the system behaves as if the
kicking strength were $\kappa ^2$ rather than $\kappa$. For $E=0$, SWC is known
to be a classical fingerprint of quantum antiresonance but it occurs under much
less generic conditions, in particular only for very special kicking
potentials. Manifestations of SWC are a decrease in the instability of periodic
orbits and a narrowing of the chaotic layers, relative to the ordinary
weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic
web" in phase space, the chaotic diffusion on the web is much slower than the
weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small
$\kappa$. In some special cases, the effect is shown to cause ballistic motion
for almost all parameter values. The generic global SWC on stochastic webs in
the KHS appears to be the two-dimensional closest analog to the Arnol'd web in
higher dimensional systems.
