One reason could be envy. Maybe Naruto sees Hinata as having something he doesn't, like a more stable family situation, and he lashes out in jealousy. Another reason might be that he's just being a typical, rambunctious kid who doesn't realize the impact of his words or actions on Hinata.
One popular fanfiction might be where Hinata's bullying of Naruto is a misunderstanding. Maybe she was trying to get his attention in a really wrong way because she actually had a crush on him. For example, she could be stealing his lunch as a way to start a conversation, but Naruto takes it as bullying.
The author could introduce a backstory for Hinata's bullying. For instance, if she was bullied herself in the past and is now projecting that onto Naruto. As the fanfiction unfolds, she could face her own demons and stop bullying Naruto as she heals from her past traumas.
Well, it's not super common but it does exist. In some fanfictions, the 'Naruto bullies Hinata' scenario is used as a starting point to show character growth. For example, Naruto might start off bullying Hinata out of immaturity or misunderstanding, and then as the story progresses, he realizes his mistake and tries to make amends. This can lead to a deeper connection between them in the end.
Once upon a time, Hinata was being bullied near the training grounds. The bullies were taunting her about her shy nature. Just as they were about to get physical, Naruto showed up. He remembered all the times Hinata had been kind to him. 'You guys think it's cool to pick on someone smaller?' Naruto asked. The bullies tried to act tough but Naruto's presence was too much for them. He then turned to Hinata, 'Don't let them get to you. You're strong, Hinata.' And from that day on, Hinata felt a little braver knowing Naruto had her back.
The plot could start with Hinata being alone in a secluded part of the village and the bullies spotting her. They start to tease her about her family or her lack of confidence. Naruto, who has a strong sense of justice, comes across the scene. He uses his skills and his reputation as a hero to scare the bullies away. After that, Hinata and Naruto have a moment where Hinata thanks Naruto, and Naruto encourages her to be more assertive.
In some Naruto fanfictions, Hinata could potentially be portrayed as a 'weapon' in a very metaphorical sense. For example, her Byakugan abilities might be exploited in unique ways that make her seem like a strategic weapon for a side or a cause. But in the canon Naruto story, she is a character with her own agency and not really a weapon.
One great source for Naruto and Hinata fanfiction could be FanFiction.net. You can search for stories specifically focused on their relationship there. There are often new and interesting takes on their story, from how they first fell in love to their married life in the future.
Perhaps in the fanfiction, Hinata wears a micro bikini for a special festival in the Hidden Leaf Village. Naruto is really excited to see her in it. They participate in the festival games together and Hinata's new look makes Naruto see her in a different light, more as a strong and confident woman.
One possible fanfiction could involve Naruto learning kenjutsu skills and Hinata being inspired by his newfound abilities. Maybe Naruto discovers an ancient sword technique and Hinata supports him in his training, leading to a deeper bond between them.