  We prove that infinitely presented graphical $Gr(7)$ small cancellation
groups are acylindrically hyperbolic. In particular, infinitely presented
classical $C(7)$-groups and, hence, classical $C'(\frac{1}{6})$-groups are
acylindrically hyperbolic. We also prove the analogous statements for the
larger class of graphical small cancellation presentations over free products.
We construct infinitely presented classical $C'(\frac{1}{6})$-groups that
provide new examples of divergence functions of groups.
