Starting from the general class of super-renormalizable theories studied by M. Asorey, J.L. Lopetz, and I.L. Shapiro in 1996, we present a weakly nonlocal gravitational theory unitary and finite at quantum level in the quantum field theory framework (the theory is also compatible with causality because a Shapiro's time advance never occurs.) As a consequence of finiteness, the Weyl's anomaly is not present and the theory turns out to be conformal invariant at classical as well at quantum level. Therefore, nonlocal quantum gravity is a conformal invariant theory in the spontaneously broken phase of the Weyl symmetry. As a result, Weyl conformal symmetry solves the black hole's singularity issue and cosmological singularity problem, otherwise unavoidable in any local or non-local gravitational theory. At classical level, all Einstein manifolds are stable at linear and non linear level if they are stable in General relativity. The generalization of the theory in presence of matter is the topic of the current research, hence it will be discussed only briefly.