  Several recent studies have shown that the anisotropy in the magnetic
structure of \ECA\ plays a significant role in stabilizing the Weyl nodes. To
investigate the relationship between magnetic anisotropy and Weyl physics, we
present a comparative study between EuZn$_2$As$_2$ and EuCd$_2$As$_2$ that are
isostructural but with different magnetic anisotropy. We performed structural
analysis, electronic transport, and magnetization experiments on
millimeter-sized single crystals of EuZn$_2$As$_2$, and compared the results to
those of EuCd$_2$As$_2$. By combining the first principle calculations and
neutron diffraction experiment, we identify the magnetic ground state of
EuZn$_2$As$_2$ as A-type antiferromagnetic order with a transition temperature
($T_\mathrm{N}$ = 19.6 K) twice that of EuCd$_2$As$_2$. Like EuCd$_2$As$_2$,
the negative magnetoresistance of EuZn$_2$As$_2$ is observed after suppressing
the resistivity peak at $T_\mathrm{N}$ with increasing fields. However, the
anisotropy in both transport and magnetization are much reduced in
EuZn$_2$As$_2$. The difference could be ascribed to the weaker spin-orbit
coupling, more localized $d$-orbitals, and a larger contribution from the Eu
$s$-orbitals in the zinc compound, as suggested by the electronic band
calculations. The same band structure effect could be also responsible for the
observation of a smaller non-linear anomalous Hall effect in EuZn$_2$As$_2$
compared to EuCd$_2$As$_2$.
