Antigua was still a British colony at the time this novel is set, and this climate (both the tropical one and the Colonial one) is the backdrop to the events of this novel. There is a strong British influence on everything that happens on the island: from government down to the curriculum at school. This is, frankly, oppressive.
Maybe that's not entirely surprising—Postcolonial literature is rife with the apt thesis statement "Wow, Colonialism sure is tyrannical." But what is surprising—at least for those of us who live out half the year with frantic daydreams of tropical islands because there are no two words more horrific than "wintry mix"—is that Antigua's climate is also oppressive.
Sure, it's beautiful. There are guava trees and fresh fish every day. The sea is always nearby. The sun is already high in the sky early in the morning. But it never changes. Never. Changes. Never.
This is less a damning statement on the climate of Antigua and more a reflection of the psychological climate of our Annie John. She needs and craves change. And Antigua, with its constant stifling heat, ain't going to give her the change she craves.