Map from Google - Anguilla

Anguilla has a tropical climate, hot all year round, with a slightly cooler period from December to March, and a hotter and muggy period from May to October. Luckily, sea breezes relieve a bit the heat of the day.
Here are the average temperatures in the capital, The Valley.
Average temperatures - The Valley
The ValleyJanFebMarAprMayJunJulAugSepOctNovDec
The ValleyJFMAMJJASOND
Min (°C)232323252526262626262524
Max (°C)282828283031313131302928
Min (°F)737373777779797979797775
Max (°F)828282828688888888868482

Anguilla is located in the northernmost part of the Lesser Antilles, and it's a British overseas territory, formed by the main island, where the capital is found, plus some small coral islands.
Rainfall is generally not very abundant, since it amounts to around 1,000 millimetres (40 inches) per year. February and March are usually the driest months, with about 45 mm (1.8 in) 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 (4 and 5 in) per month. During 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, in days in which the sun shines for a few hours anyway. More rarely, there can be heavy and prolonged rains when tropical depressions and hurricanes hit the islands; this can happen, in Anguilla as in other Caribbean islands, from June to November (but especially from August to October).
Here is the average precipitation.
Average precipitation - The Valley
The ValleyJanFebMarAprMayJunJulAugSepOctNovDecYear
The ValleyJFMAMJJASONDY
Prec. (mm)65454565956075100130110125901005
Prec.(in)2.61.81.82.63.72.433.95.14.34.93.539.6
Days1087810891213121312122

The amount of sunshine is good all year round, as can be seen in the following table.
Sunshine - The Valley
The ValleyJanFebMarAprMayJunJulAugSepOctNovDec
The ValleyJFMAMJJASOND
Sun (hours)889988898888

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
Sea (°F)797979798182828284848281

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 driest 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.