Hodaka Morishima is an important character. He is a young boy who runs away from his home on an island to Tokyo. His journey forms a major part of the story as he tries to find his place in the big city. Then there is Hina Amano. She has the special ability to stop the rain and clear the sky, which makes her a central figure in the events related to the abnormal weather.
The themes of youth and growing up are prominent. The young protagonists face challenges that force them to mature quickly. They learn about responsibility as they deal with the strange weather phenomena. Also, love is a key theme. The relationship between the main characters is developed in the context of the chaotic weather, and their love has to endure many difficulties.
Some fanfictions might focus on the idea of a different world - building. In the movie, Tokyo is the main setting. But in fanfiction, the story could be set in a different city or even a completely different world where the rules of weather are even more extreme. There could also be a concept of shared powers among more people rather than just Hina. This would change the dynamics of the story completely and create new plotlines and relationships.
I'm not sure specifically as there could be many stories related to weathering waves. It might be about how something endures or is affected by the continuous action of waves, perhaps a story of a coastal structure or a creature's struggle against the waves.
Hodaka and Hina are definitely the most popular. Since they are the main characters in the original, fanfiction writers love to explore their relationship further. They might write about their future together or create alternate scenarios for their first meeting.
In a 'weathering waves story', if it's about a coastal community, the main characters could be the fishermen. They are constantly out at sea, facing the power of the waves every day. Their boats are also like characters in a way, as they are the vessels that have to withstand the waves' force. Another possible main character could be a marine biologist who studies the organisms in the area affected by the waves, and how they adapt to the changing environment due to wave action.