Batanes has a narrow window of reliably good weather, and timing your visit around it makes a significant difference.
March to May is the best time to go. The skies are mostly clear, the seas are calm enough for inter-island boat trips, and the rolling hills are a vivid green from earlier rains. This is when you are most likely to get smooth flights, functioning boat services to Sabtang and Itbayat, and dry days for walking. It is also when Batanes sees its most visitors, though crowded is a relative term here.
June to December is typhoon season. Batanes sits directly in the track of typhoons forming in the Pacific, and the islands typically absorb several strong storms each year. This is not the time to visit unless you are very flexible with your schedule. Flights are cancelled, boats stop running, and there are periods when the islands are effectively cut off. The Ivatan houses were built to survive exactly this — but a traveller's hotel room was not designed for weeks of waiting.
January and February bring cold, persistent wind from the north — the amian season. Temperatures drop to the low teens at night and the wind rarely lets up. The landscape can be dramatic and misty, but boat crossings are rough and the cold is more than many visitors expect from the Philippines.
If your dates are fixed and fall outside March–May, the islands are still worth visiting — just go with low expectations for inter-island travel and be prepared for weather delays.