This, coupled with a "modern" lifestyle of less and less manual labor results in an overabundance of unspent caloric intake. As the article in [2] says, which specifically talks about Micronesia but is applicable elsewhere in the Pacific:
"Micronesians are essentially selling their own natural food resources for a fraction of the true value, and then using the revenue to import nutrient-poor food (...) The FSM does not have the infrastructure to realistically compete in the global tuna market. Thus, the current structure of the Pacific tuna industry is an example of how lack of development (partly due to the U.S subsidies and U.S. dependence) has lead the FSM to continue to be dependent on foreign nations. The cash-economy stemming from the tuna industry contributes to the continued cycle of food dependence, imported-food, and poor diet, which is partly responsible for Micronesia's unhealthy, obese population."
Edit: As with regard to Vanuatu specifically, you can read a report on their food, agriculture, and fishery situation here [3], authored by FAO of the UN. To paraphrase, widespread industrial fishing by foreign nations was prevalent decades ago, but has since shifted to other Pacific states. Subsistence fishing occurs, but the cash-based economy (i.e. where you buy your food, rather than catch it) is much larger, and the presence of tourism sites has priced most locals out of domestically-caught fish, while leaving imported chicken and domestic beef affordable, as well as imported canned fish. This report doesn't mention foods typically considered junk food, but calorie-dense imports of shelf-stable food are documented elsewhere.
[1] http://www.nature.com/ng/journal/v48/n9/full/ng.3620.html [2] https://globalizationandhealth.biomedcentral.com/articles/10... [3] http://www.fao.org/fi/oldsite/FCP/en/VUT/profile.htm