  The hallmark of nematic order in iron-based superconductors is a resistivity
anisotropy but it is unclear to which extent quasiparticle dispersions,
lifetimes and coherence contribute. While the lifted degeneracy of the Fe
$d_{xz}$ and $d_{yz}$ dispersions has been studied extensively, only little is
known about the two other factors. Here, we combine in situ strain tuning with
ARPES and study the nematic response of the spectral weight in BaFe$_2$As$_2$.
The symmetry analysis of the ARPES spectra demonstrates that the $d_{xz}$ band
gains quasiparticle spectral weight compared to the $d_{yz}$ band for negative
antisymmetric strain $\Delta \epsilon_{yy}$ suggesting the same response inside
the nematic phase. Our results are compatible with a different coherence of the
$d_{xz}$ and $d_{yz}$ orbital within a Hund's metal picture. We also discuss
the influence of orbital mixing.
