  It has been recently argued that Higgsing of theories with $U(1)^n$ gauge
interactions consistent with the Weak Gravity Conjecture (WGC) may lead to
effective field theories parametrically violating WGC constraints. The minimal
examples typically involve Higgs scalars with a large charge with respect to a
$U(1)$ (e.g. charges $(Z,1)$ in $U(1)^2$ with $Z\gg 1$). This type of Higgs
multiplets play also a key role in clockwork $U(1)$ theories. We study these
issues in the context of heterotic string theory and find that, while indeed
there is no new physics at the standard magnetic WGC scale $\Lambda\sim g_{IR}
M_P$, the string scale is just slightly above, at a scale $\sim
\sqrt{k_{IR}}\Lambda$. Here $k_{IR}$ is the level of the IR $U(1)$ worldsheet
current. We show that, unlike the standard magnetic cutoff, this bound is
insensitive to subsequent Higgsing. One may argue that this constraint gives
rise to no bound at the effective field theory level since $k_0$ is model
dependent and in general unknown. However there is an additional constraint to
be taken into account, which is that the Higgsing scalars with large charge $Z$
should be part of the string massless spectrum, which becomes an upper bound
$k_{IR}\leq k_0^2$, where $k_0$ is the level of the UV currents. Thus, for
fixed $k_0$, $Z$ cannot be made parametrically large. The upper bound on the
charges $Z$ leads to limitations on the size and structure of hierarchies in an
iterated $U(1)$ clockwork mechanism.
