To see Diamond's evidence, you need to look in Part Three of the book, particularly Chapters 12 through 14. This part of the book is entitled "From Food to Guns, Germs, and Steel." This means that it explains the way that food production (agriculture) leads to things like writing, technology, and complex government. These can be seen as types the "societal development" that you ask about.
In these chapters, Diamond offers evidence from all over the world to defend his claims. He cites, for example, the connection between agriculture and writing in Sumer, Mexico, and China. He argues that areas that had food production from early times developed technology sooner. Finally, he uses societies from Hawaii to South Africa as evidence that agriculture leads to complex systems of government.
The evidence that Diamond offers is spread over these three chapters and includes references to many different societies.