Map from Google - Tuvalu

Tuvalu, Oceanian archipelago located south of the equator, has an equatorial climate, ie hot, humid and rainy throughout the year. The rains, occurring in the form of downpours of thunderstorms, do not last long and do not greatly reduce the hours of sunshine.
The temperatures are very stable throughout the year, around 25 °C at night, and 31 °C during the day. The trade winds blow throughout the year, but especially during the period from April to October, tempering a little the heat.
Here are the average temperatures of the capital Funafuti.
Average temperatures - Funafuti
FunafutiJanFebMarAprMayJunJulAugSepOctNovDec
FunafutiJFMAMJJASOND
Min (°C)252525252525252525252525
Max (°C)313131313131313131313131

Precipitation is definitely abundant, since it exceeds 3,000 millimetres per year.
In the capital Funafuti, 3,200 mm of rain per year fall, with a peak between December and March, when they are equal to or greater than 300 mm per month, and a minimum (very relative...) between May and October, when they drop below 250 mm per month. Here is the average precipitation.
Average precipitation - Funafuti
FunafutiJanFebMarAprMayJunJulAugSepOctNovDecYear
FunafutiJFMAMJJASONDY
Prec. (mm)3603153152502352052352302002402753353190
Days181820191919202019191817226

In the northernmost islands, the rainfall is slightly less abundant.
Tuvalu are affected by the tropical cyclones of the Southern Hemisphere, in the period November to mid-May (although sometimes they have occurred outside of this period, as happened with Bebe on late October 1972, and Keli in June 1997). Being not far from the equator, the islands are generally affected by cyclones at the beginning of their formation, but considering that Tuvalu is one of the flattest countries in the world, cyclones can cause flooding, but also storm surges, even if they are not are very strong or if they pass at a certain distance. The northernmost islands (Nanumea, Niutao, Nanumanga), closer to the equator, are located at the edge of the area, where cyclones are rare.

Funafuti

For swimming, the sea is warm all year round, as we can see in the following table.
Sea temperature - Funafuti
FunafutiJanFebMarAprMayJunJulAugSepOctNovDec
FunafutiJFMAMJJASOND
Sea (°C)292929303029292929293030


When to go

The best time to travel to Tuvalu is from mid-May to late October, being a relatively less rainy period, and out of the cyclone season. Since sometimes there have been cyclones outside of the canonical period, to go on the safe side, you can choose the period from July to mid-October.

What to pack

All year round, tropics-friendly, loose fitting clothing, sun hat, a scarf for the breeze, a light sweatshirt for the evening, light raincoat or umbrella.