Map from Google - British_Virgin_Islands

The climate in the British Virgin Islands is tropical, hot throughout the year, and also influenced by the trade winds, with a more pleasant period, from December to March, when the daily average temperature is around 24/25 °C (75/77 °F), and a hotter and sultry period, from May to October, when the daily averages are around 28 °C (82 °F).
The British Virgin Islands are located in the Caribbean Sea, in the Lesser Antilles. The main islands are Tortola, Anegada and Virgin Gorda.
Here are the average temperatures of Road Town, the capital, in the island of Tortola.
Average temperatures - Road Town
Road TownJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)212121222324242424242322
Max (°C)282828292930303131302928
Min (°F)707070727375757575757372
Max (°F)828282848486868888868482

As regards the rainfall, there is a relatively dry season from January to April, and a rainy season from May to December, the latter having a relative decrease in June and July. The least rainy months, in which precipitation doesn't go above 50 millimetres (2 inches) per month, are February and March. The annual amount of rainfall is around 1,000/1,200 mm (40/47 in) per year, and generally is slightly more abundant in the northern slopes of each island, in particular those with hills or low mountains in inland areas, such as Tortola and Virgin Gorda.
In April and May there's an increase in rainfall, although in June and July there is often a new relative decrease, followed by a recovery from August to November. Generally, the wettest period goes from September to November.
Here is the average precipitation.
Average precipitation - Road Town
Road TownJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)705050601057585110145145130801105

From June to November these islands can be affected by hurricanes and tropical storms, as happens throughout the Antilles. Apart from hurricanes, which can bring strong winds and torrential rains but fortunately occur rarely, normally the weather is nice or variable, interrupted by brief showers and thunderstorms, more likely and more intense during the rainy season, which means that in any case the sun shines all year round, as you can see in the following table.
Sunshine - Road Town
Road TownJanFebMarAprMayJunJulAugSepOctNovDec
Sun (hours)889988998877

Virgin Gorda

For swimming, the sea is warm all year round, about 26 °C (79 °F) from January to April, and 29 °C (84 °F) in September and October, as we can see from the water temperatures at Anegada.
Sea temperature - Anegada
Sea (°C)262626262728282829292827
Sea (°F)797979798182828284848281

When to go

The best time to visit the British Virgin Islands runs from December to April, being the least rainy and the least muggy. Within this period, the months of January, February and March are the driest and the least hot of all. In summer, June and July are generally less rainy than August and September, and have also a lower risk of tropical storms and hurricanes, which are most likely between August and October, that is, when the sea is warmer.

What to pack

From December to April: light clothes, possibly a scarf for the breeze and a sweatshirt for the evening.
From May to November: lightweight clothing, possibly a light sweatshirt and a light raincoat for thunderstorms; sweatshirt and pashmina for air-conditioned places.