Various types of fat are not equally fattening. While saturated fats and omega-6 polyunsaturated fats contribute to obesity. Omega-3 and, to a lesser extent monounsaturated fats, are negatively correlated with obesity.
A large, ecological study using data over five years and including 168 countries found that obesity rates were related to caloric intake, total fat intake, saturated fat intake and polyunsaturated fat intake….but not monounsaturated fat intake. In fact, the higher the intake of monounsaturated fat, the lower the obesity rate.
Unfortunately, the study did not break down polyunsaturated fat into omega-3 and omega-6. But since most of the polyunsaturated fats that are consumed are omega-6, it is not a suprise that they had a negative impact in this study.