1kg of fat would be 9000 kcal. Impressive energy expenditure there. Of course a lot of water weight is lost initially (when fasting or just skipping all carbs) but that rate won't hold for weeks on end.
I thought in ketosis it wasn't energy expenditure, the liver causes fat to break down and pass through your bladder? ... maybe I have that all back to front though :\ Maybe ketones pass through your bladder and they also break down fat cells...
In the absence of metabolic disease, the body breaks down fat to use the resulting energy. Think about it evolutionarily; "there's no food right now, time to jettison my energy stores"?
Ketosis is a pretty weird state brought on by lack of carbohydrates. The liver starts producing ketones, ketones rapidly breakdown fat cells to boost blood sugar.
It is mostly unrelated to diabetes as that relates to insulin response.