This is an interesting topic to me, the reason why is because everyone on the mainland has this perception that everyone in the Caribbean eats super well and everything is so fresh and green - while it is true to an extent and these things are available; it's just not common. The education here is really bad straight up; with nutrition information, it's really bad. White rice, artificial flavor additions, recycled cheap oils and beers. Cheese with bread, sugary pre-packed candy, milk and a bread before bed on top of a culture that hates exercise or any idea of walking. There is this cultural hesitation around exercise and pushing hard I hardly see anyone sweat unless it's from Zumba or kickboxing.
Diabetes is normal here; it affects many. I know a 23-year-old family member who was pre-diabetic, all older family members are pretty much diabetic with high blood pressure and cholesterol. I listen to most people go up the stairs and it sounds like they need oxygen I use to try and educate them by showing them some nutrition sites and explaining to them about a balanced diet since I have been bodybuilding since I was 15 they don't really listen so I have stopped. It amazes some family members that people pay to go "work" out like you're losing and the gym is winning or something.
It's quite sad really cause healthy communities are paramount to a healthy functioning society but both education and motivation is lacking and the last one is a bit harder to change in the situation.
If you have the space try to grow something. even on the roof you could set up a little project ? I am trying to grow some veggies currently and have been getting other seedlings ready, I really would like to try and get my own fish if I have a chance and find a spot on the north coast

anyways, I understand you, don't be afraid to say no to their offers, the food def will not go to waste here..