  We study the stability and spectrum of BPS states in ${\cal N}=2$
supergravity. We find evidence, and prove for a large class of cases, that BPS
stability exhibits a certain filtration which is partially independent of the
value of the gauge couplings. Specifically, for any perturbative value of any
gauge coupling $g \ll 1$, a BPS state can only decay to some constituents if
those constituents do not become infinitely heavier than it in the vanishing
coupling limit $g \rightarrow 0$. This stability filtration can be
mathematically formulated in terms of the monodromy weight filtration of the
limiting mixed Hodge structure associated to the vanishing coupling limit. We
study various implications of the result for the Swampland program which aims
to understand such weak-coupling limits, specifically regarding the nature and
presence of an infinite tower of light charged BPS states.
