  We study a non-universal flavor scenario at the level of the Standard Model
Effective Field Theory, according to which the matrix of Wilson coefficients
$c_{uW}$ of an up-type electroweak quark dipole operator is aligned with the
up-type Yukawa coupling. Such an alignment usually follows from the assumption
of Minimal Flavor Violation (MFV), away from which we step by allowing the
entries of $c_{uW}$ to be sizable along the first quark generations. A
particular example, which we refer to as ``inverse hierarchy MFV", features
Wilson coefficients inversely proportional to quark masses, and arises from BSM
models respecting MFV and containing heavy fields that replicate the mass
hierarchy of SM quarks. We then analyze the phenomenology driven by $c_{uW}$ at
colliders and at lower-energy flavor experiments. We show that precision
measurements of the process $pp\rightarrow W h\rightarrow \gamma\gamma\ell\nu$
at FCC-$hh$ could set an upper bound on
$|c_{uW}|\lesssim\mathcal{O}(10^{-2})(\Lambda/{\rm TeV})^{2}$, with $\Lambda$
the cutoff of the effective field theory. This bound is an order of magnitude
stronger than the existing LHC bounds. Moreover, we estimate that $W
h\rightarrow b\bar b \ell\nu$ at HL-LHC could also give competitive bounds. In
the low-energy regime, we consider bounds arising from rare kaon decays, which
turn out to be loose, $|c_{uW}^{11}|<\mathcal{O}(1)(\Lambda/{\rm TeV})^{2}$. We
finally demonstrate that our flavor and operator assumptions can be derived
from a weakly-coupled UV model, which we choose to simultaneously illustrate
the UV origin of inverse hierarchy MFV.
