Map from Google - Anguilla

Anguilla has a tropical climate, hot all year round, with a good amount of sunshine and temperatures consistently above 20 °C at night and around 30 °C during the day, a little lower, around 28/29 °C in the "winter" months, and higher, around 31/32 °C in the "summer" months. During the latter period, from May to October, the slightly higher temperatures make the heat more uncomfortable, especially because of the air moisture, which is, however, high throughout the year. Luckily, the sensation of heat is reduced by the breezes.
Average temperatures - The Valley
The ValleyJanFebMarAprMayJunJulAugSepOctNovDec
The ValleyJFMAMJJASOND
Min (°C)232323252526262626262524
Max (°C)282828283031313131302928

Anguilla is part of the Caribbean, and it's a British overseas territory, formed by the main island, where lies the capital The Valley, plus some small coral islands.
Rainfall is generally not very abundant, since it amounts to around 1,000 millimetres per year. February and March are usually the driest months, with about 45 millimetres per month on average, while in the rest of the year the rains are quite irregular, although they rarely reach high values. Normally the rainy period goes from August to November, however, with moderate rainfall, between 100 and 130 mm per month. In some years there may be another peak of precipitation in April and May. As normally happens in tropical areas, the rains usually fall in the form of downpour or thunderstorm, which interrupt the sunny days; more rarely, there can be heavy and prolonged rains when tropical depressions and hurricanes hit the islands, which can happen from June to November (but especially from August to October) in Anguilla as in other Caribbean islands.
Here is the average precipitation.
Average precipitation - The Valley
The ValleyJanFebMarAprMayJunJulAugSepOctNovDecYear
The ValleyJFMAMJJASONDY
Prec. (mm)65454565956075100130110125901005
Days1087810891213121312122

Anguilla

The sea in Anguilla is warm enough for swimming all year round, although of course it's a bit warmer in the summer months.
Sea temperature - The Valley
The ValleyJanFebMarAprMayJunJulAugSepOctNovDec
The ValleyJFMAMJJASOND
Sea (°C)262626262728282829292827

When to go

The best time to visit Anguilla runs from December to April, when the temperatures are a bit lower and we are outside of the hurricane season, and particularly in February and March, which are the least rainy months. In summer, June and July are usually a bit less rainy than August, and also have a lower probability of hurricanes.

What to pack

From December to April: light clothing, a light sweater or sweatshirt for the evening and for the breeze.
From May to November: lightweight, loose fitting clothing, possibly a light sweatshirt and a light raincoat for thunderstorms.
For the reef, equipment for snorkeling, water shoes or rubber soled shoes.