Map from Google - Saint_Kitts_and_Nevis

The climate in St. Kitts and Nevis is tropical, hot and humid all year round.
Saint Kitts and Nevis is a state of the Lesser Antilles, formed by two islands of the same name, and the capital city is Basseterre.
The daily average temperature is around 25 degrees Celsius (77 °F) in January and February, and 28 °C (82 °F) from June to October, which is the hottest period. Sea breezes temper the heat in the summer months, which however is definitely muggy.
Here are the average temperatures of Basseterre.
Average temperatures - Basseterre
BasseterreJanFebMarAprMayJunJulAugSepOctNovDec
BasseterreJFMAMJJASOND
Min (°C)222223232425252525252423
Max (°C)282829293031313131313029
Min (°F)727273737577777777777573
Max (°F)828284848688888888888684

Rainfall amounts to around 1,200 millimetres (47 inches) per year along the coast. The rainiest period, in which precipitation exceeds 100 mm (4 in) per month, runs from July to November, while the driest runs from February to April, when rainfall does not exceed 60 mm (2.4 in) per month. The rains, as it's normally the case in countries having a tropical climate, occur primarily in the form of downpour or thunderstorm, so they do not reduce too much the hours of sunshine, and are quite irregular, which means that there may be periods without rainfall in every month of the year, but also periods of heavy rains for several consecutive days.
Here is the average precipitation.
Average precipitation - Basseterre
BasseterreJanFebMarAprMayJunJulAugSepOctNovDecYear
BasseterreJFMAMJJASONDY
Prec. (mm)905055609085115130140125130901160
Prec.(in)3.522.22.43.53.34.55.15.54.95.13.545.7
Days129981010131414131513140

In each of the two islands there is a volcano: Mount Liamuiga, former Misery, 1,156 metres high, and Nevis Peak, 985 metres high; on their slopes the climate is very humid, with more abundant rainfall than on the coast, so that above 900 metres (3,000 feet), the vegetation becomes lush and a cloud forest grows.

From June to November, like in the whole area of the Caribbean and the West Indies, there is the danger of tropical storms and hurricanes, with greater probability from August to October.

Nevis

The sea in Saint Kitts and Nevis is warm enough for swimming all year round, as we can see from the following table.
Sea temperature - Basseterre
BasseterreJanFebMarAprMayJunJulAugSepOctNovDec
BasseterreJFMAMJJASOND
Sea (°C)262626272728282829292827
Sea (°F)797979818182828284848281

When to go

The best time to visit Saint Kitts and Nevis goes from December to April, being the least hot, and also outside the period of hurricanes; within this period, in particular, February and March stand out, as the driest months by far. In the summer months, the weather is hot and sultry, and thunderstorms are more common, although they rarely lead to very heavy rains; however, in August and September there's a greater risk of heavy rains than in June and July. Anyway, the greatest danger in the long summer in the Caribbean, comes from hurricanes.

What to pack

From December to April: light clothing, a light sweatshirt for the evening.
From May to November: lightweight clothing, possibly a light sweatshirt and a light raincoat for thunderstorms.