Map from Google - Cayman_Islands

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; their capital is George Town. Their climate is tropical, hot and humid all year round, with a dry and relatively cool season from late November to mid-April, and a rainy and muggy season, from late April to early November. Precipitation amounts to about 1,400 millimetres per year, and the rainiest months are September and October.
Here is the average precipitation in George Town.
Average precipitation - George Town
George TownJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)50403530150160145150220220155701425

During the rainy season, the maximum temperature is around 32 degrees Celsius, and moisture makes the heat sweltering, even though the breezes temper it a bit. 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, the tropical cyclones of the Caribbean. The hurricane season runs from June to November, but the period in which they are most likely runs from August to October.
In winter, the 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 may bring nighttime temperatures to below 20 °C.
Here are the average temperatures.
Average temperatures - George Town
George TownJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)202020222324242424232221
Max (°C)282929303132323232313029

Grand Cayman

Even the sea is warm, not going below 27 °C, as we can see from the following table.
Sea temperature - Cayman
Sea (°C)272727272829292929292828

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 the more dangerous but fortunately rare hurricanes.

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.