  Recently it has been shown that the cosmological dynamics of covariant $f(Q)$
gravity depend on different affine connections. In this paper, two specific
$f(Q)$ models are investigated with SNe+CC+BAO+QSO observational data, and the
spatial curvature of the universe is studied in covariant $f(Q)$ gravity. It is
found that the parameters $\mathcal{X}_0$ and $\mathcal{X}'_0$ characterizing
affine connections significantly affect the behavior of the effective equation
of state $w_Q$ and may drive it across the phantom divide line. These results
imply some inertial effects of the universe change the cosmic dynamics. However
based on the Bayesian evidence, the zero inertial effect is more favored in the
flat universe. Moreover, a closed universe is favored not only in the
$\Lambda$CDM model but also in covariant $f(Q)$ gravity. The $f(Q)$ models have
less support evidence than the $\Lambda$CDM model in the non-flat universe.
