starting in 1600 BC describe the groups who controlled Babylon and how each group or person came to power.​

Babylonia, or Babylon, as some people call it, was a very small city in Southern Mesopotamia, which stood alongside other cities from the earlier Akkadian Empire, like Ur, Kish and Uruk, just to name a few.
Around 1894 BC, however, it was a group called the Amorites, who took control of the city and began to organize it. Exactly in 1894, a dynasty from the Amorites formed a small kingdom called Kazallu, which would later on start to expand and change as subsequent Amorite rules took over control. Babylonia was the center of this small kingdom. There were many rulers who consistently helped Babylonia to develop and grow into an independent nation. The first such ruler, not yet named king, was Sumu-abum, followed by several others, until the first Amorite who called himself king: Sin-Muballit. It was in 1792 BC, that things changed in Babylonia, and it became a pretty powerful, but short-lived empire, under the rule of Amorite leader and king Hammurabi. It was this man who was responsible for the development and growth of the Babylonian Empire and its extension throughout most of Mesopotamia, alongside the much older Assyrian Empire.