  We study the charge-to-mass ratios of BPS states in four-dimensional
$\mathcal{N}=2$ supergravities arising from Calabi-Yau threefold
compactifications of Type IIB string theory. We present a formula for the
asymptotic charge-to-mass ratio valid for all limits in complex structure
moduli space. This is achieved by using the sl(2)-structure that emerges in any
such limit as described by asymptotic Hodge theory. The asymptotic
charge-to-mass formula applies for sl(2)-elementary states that couple to the
graviphoton asymptotically. Using this formula, we determine the radii of the
ellipsoid that forms the extremality region of electric BPS black holes, which
provides us with a general asymptotic bound on the charge-to-mass ratio for
these theories. Finally, we comment on how these bounds for the Weak Gravity
Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture
and Swampland Distance Conjecture.
