Why cruisers favoured 9.2-inch guns

Why did so many navies use 9.2-inch cruiser guns?

They offered a powerful step above eight-inch guns while avoiding many of the weight and handling penalties associated with ten- or twelve-inch weapons.

The 9.2-inch gun was a useful cruiser compromise. An eight-inch weapon remained easy enough to handle but gave up a noticeable amount of striking power. A ten-inch gun began to impose the weight and handling penalties associated with battleship weapons, at which point a navy might as well consider twelve inches. The 9.2-inch calibre occupied the useful space between those choices. It offered substantially greater effect than an eight-inch gun while preserving a similar practical rate of fire and avoiding a battleship-scale installation.