According to Wikipedia, the reasons for obesity in the Pacific islands are:
A large part of the local diet consists of processed, high-calorie and imported foods, such as spam or corned beef, rather than fresh fish, fruits and vegetables, in part because the mining past has reduced the amount of arable land . Unhealthy foods are sold on the Pacific islands due to the region's relative poverty.
Relatively sedentary lifestyle, including among children.
Cultural factors, including:
History of poor public education on diets, exercise and health (micronutrient deficiencies are also common);
Banquets and parties continue to be a big part of life;
Imported foods have a higher social status than healthier local foods;
Historically, having a great body is associated with wealth, power and beauty.
High rates of obesity begin to appear 15 months after birth.