Map from Google - Christmas_Island

The climate of the Cayman Islands is tropical, hot and humid all year round, with a dry and relatively cool season from late November to mid-April, in which the northeast trade winds blow, and a rainy and muggy season from late April to early November.
The three Cayman Islands (Grand Cayman, Little Cayman and Cayman Brac), are located in the Caribbean Sea, south of Cuba, and belong to the British crown; the capital is George Town.
Precipitation amounts to about 1,400 millimetres (55 inches) per year, and the rainiest months are September and October.
Here is the average precipitation in George Town.
@prec-George Town
During the rainy season, the maximum temperature is around 32 degrees Celsius (90 °F), and moisture makes the heat sweltering, although sea breezes give some relief. Rainfall occurs mainly in the form of showers and thunderstorms in the evening, which is typical of many countries having a tropical climate, so there is still a fairly good amount of sunshine. Anyway, every now and then the islands can be hit by hurricanes, tropical cyclones of the Caribbean and the Atlantic. The hurricane season runs from June to November, but the period in which they are most likely runs from August to October.
In winter, temperatures in the Caymans are lower than in summer, but they are still high enough for swimming and sun bathing. However, from December to March the islands can sometimes be affected by cool winds from the United States, which can lower the night temperature below 20 °C (68 °F).
Here are the average temperatures.
@temp-George Town
Grand Cayman

The sea is warm all year round, not going below 27 °C (81 °F), as we can see from the following table.
When to go

The best time to visit the Caymans runs from late November to mid-April, because it's the least hot and the least rainy. During the hot and muggy summer, heavy showers and thunderstorms are possible, as well as hurricanes, which are more dangerous but fortunately rare.

What to pack

From November to April: light clothes, a sweatshirt for the evening.
From May to October, tropics-friendly, lightweight clothing, possibly a light sweatshirt and a light raincoat for thunderstorms.