Perhaps Carlisle is aware of the emotional turmoil Bella is going through regarding her relationship with Edward or her new life among vampires. By wiping her tears, he is trying to show her that she is not alone and that he is there to support her. He might also be trying to prevent her from making hasty decisions out of extreme emotions.
Maybe Carlisle wipes Bella's tears because he sees her as a vulnerable human in a dangerous supernatural world. He has a kind heart and wants to comfort her.
It could be that Carlisle has a fatherly affection towards Bella. He might sense her fear or sadness and his natural instinct is to offer some form of solace, so he wipes her tears.
Often, it starts with an unexpected encounter or a moment of realization. Maybe Carlisle sees Bella in a new light, not just as Edward's girlfriend but as an individual with her own charm. Then, there are small gestures of kindness and understanding between them that gradually build up the relationship.
One possibility in such a fanfiction could be that their relationship completely alters the dynamics of the original Twilight story. For example, it might change how the Cullen family functions and their interactions with other characters. Maybe Bella's connection with Carlisle would lead to a different approach in dealing with the Volturi.
In some fanfictions, there could be a grand display of the Cullen family's unity. They might have a party filled with elegant decorations, like twinkling lights and beautiful floral arrangements. There could be a special dance between Carlisle and Bella, and the other Cullens would be happily celebrating around them.
Another aspect could be the exploration of the vampire - human relationship in a different light. With Bella and Carlisle, it's not the typical young vampire - young human love story like Bella and Edward. It might delve deeper into the more mature and complex aspects of a relationship between a much - older vampire and a human.
At first, it would be a bit awkward as Bella adjusts to her new life. But Carlisle would be very patient and understanding, like a father figure. Esme would be more of a motherly presence, always there to comfort Bella. As time goes on, they would become closer. Carlisle might teach Bella about the vampire history and ethics, and Esme would share her love for the family and home. Eventually, they would have a very strong, loving bond.
He becomes more vulnerable. Usually, Carlisle is seen as this strong, composed leader. But when he falls in love with Bella, his emotions start to get the better of him at times. He might second - guess his decisions more often.
She might feel a sense of comfort. Since Carlisle is an authoritative and kind figure, his gesture could make Bella feel safe.
The Cullen family members are important characters too. Edward, for example, might have an interesting dynamic with Bella in this fanfiction. He could be either protective or jealous of Carlisle's special relationship with her.
In the fanfiction, Carlisle's sense of duty to his family and the vampire code might be a hurdle. He has to balance his feelings for Bella with his responsibilities to the Cullen family. Also, Bella's own human life and her relationships with other humans, like her father, could be a complication. How can she maintain those relationships while being in love with Carlisle? There's also the issue of secrecy. Their relationship has to be kept hidden from the outside world to protect both of them.
Carlisle could be very patient with Bella. Since he's an old and wise vampire, he might understand that her possessiveness stems from her deep love for him. He could introduce her to more of his world, hoping that by expanding her understanding, she'll become less possessive. He might also set some boundaries gently, like 'Bella, I need my own space sometimes to attend to my duties.' And if she oversteps, he'll remind her firmly but lovingly.