  Motivated by the recent CDF measurement of the $W$-boson mass, we study
string-based particle physics models which can accommodate this deviation from
the Standard Model. We consider an F-theory GUT in which the visible sector is
realized on intersecting 7-branes, and extra sector states arise from a probe
D3-brane near an E-type Yukawa point. The D3-brane worldvolume naturally
realizes a strongly coupled sector which mixes with the Higgs. In the limit
where some extra sector states get their mass solely from Higgs vevs, this
leads to a contribution to the $\rho$ parameter which is too large, but as the
D3-brane is separated from the 7-brane stack, this effect is suppressed,
leading to O(1) - O(10) TeV scale extra sector states and a correction to
$\rho$ which would be in accord with the CDF result. We also estimate the
contribution to the oblique electroweak parameter $S$, and find that it is
compatible with existing constraints. This also leads to additional signatures,
including diphoton resonances (as well as other diboson final states) in the
O(1) - O(10) TeV range.
