From General Relativity by Weinberg p.797 edited by Hawking & Israel:

This is to be used to generate a perturbation series in powers of $GE^2$ or $G/r^2$ (where $E$ and $r$ are an energy and a length that are characteristic of the process under study)

From Quantum Field Theory in a Nutshell by Zee p.172:

We come to the same morose conclusion that the theory of gravity, just like Fermi’s theory of weak interaction, is nonrenormalizable. To repeat the argument, if we calculate graviton-graviton scattering at energy $E$, we encounter the series $\sim[1+ G_NE^2 + (G_NE^2)^2 + ...]$.

I'm just looking for a brief explanation for this type of expansion or some resource where I can understand why it is in this specific form.