A fatty liver may trigger insulin resistance, which can lead to type 2 diabetes. And eating too much saturated fat or sugar may create more liver fat than eating too much unsaturated fat. Researchers randomly assigned 38 people to eat an extra 1,000 calories a day of saturated fat (from butter, cheese, and coconut oil), unsaturated fat (largely from olive oil, pesto, and pecans), or sugar (from candy, a sugary drink, and orange juice).