The British economy depended on the Caribbean
From Book: “The War for America” – by Piers Mackesy.
For the British, the American Revolution quickly became a naval war with France over possession of the islands of the Caribbean. With their vast sugar plantations, these were more lucrative to Britain than the American colonies and more likely to remain colonies over the long run. Furthermore, the French had lost key Caribbean possessions to Britain during the recent French and Indian War that had ended in 1763, and viewed the American Revolution as their opportunity to regain them:
“Why this obsession [of the British] with the West Indies? [Lord] Sandwich had predicted that the war aims of France would be to overturn the peace of 1763 and regain her empire and her markets; and that for the sake of the American alliance she would forget her claim to Canada, and look for her reward in the sub-tropics — in India, West Africa and the Caribbean. And he was right.