  We argue a smallness of gauge couplings in abelian quiver gauge theories,
taking the anomaly cancellation condition into account. In theories of our
interest there exist chiral fermions leading to chiral gauge anomalies, and an
anomaly-free gauge coupling tends to be small, and hence can give a non-trivial
condition of the weak gravity conjecture. As concrete examples, we consider
$U(1)^{k}$ gauge theories with a discrete symmetry associated with cyclic
permutations between the gauge groups, and identify anomaly-free $U(1)$ gauge
symmetries and the corresponding gauge couplings. Owing to this discrete
symmetry, we can systematically study the models and we find that the models
would be examples of the weak coupling conjecture. It is conjectured that a
certain class of chiral gauge theories with too many $U(1)$ symmetries may be
in the swampland. We also numerically study constraints on the couplings from
the scalar weak gravity conjecture in a concrete model. These constraints may
have a phenomenological implication to model building of a chiral hidden sector
as well as the visible sector.
