A great fanfiction plot could be that Faunus Ruby is being discriminated against by some students at Beacon. Weiss, who is used to a world of privilege, decides to stand up for Ruby. This act of kindness makes Ruby trust Weiss more. As time passes, they find themselves relying on each other more and more during combat and in their studies, and a beautiful friendship (or maybe something more) starts to develop.
One idea could be a story where Ruby, as a Faunus, has to hide her identity in a world that's still somewhat prejudiced against Faunus. Weiss discovers her secret and at first is conflicted because of her family's traditional views. But as they go on adventures together, Weiss realizes that Ruby is still the same brave and kind person she always knew, and they form an even deeper bond.
Perhaps Ruby made a decision that Weiss strongly disagreed with regarding a mission objective. Ruby thought it was a good idea to help a group of civilians first, but Weiss believed they should focus on the main target. Weiss would yell, 'Ruby, you're being naive! We can't deviate from our mission just for some strangers!' This would start a heated debate between them, with the other team members having to step in to calm them down.
A fanfic could be set in an alternate universe where Ruby and Weiss are not in their normal teams. They meet by chance in a new kingdom and team up to fight against a local tyrant. Along the way, they discover new things about themselves and each other. Weiss might teach Ruby some more refined combat techniques, while Ruby shows Weiss how to be more spontaneous.
Another theme is growth. Both Ruby and Weiss are on their own paths of development, and in fanfics, their relationship can play a part in that. They might learn from each other's strengths and weaknesses, like Weiss teaching Ruby about discipline and Ruby teaching Weiss about having more fun.
I'm not sure if there is such specific fanfiction readily available. Fanfiction varies greatly, and while there may be a large body of RWBY fanfiction, this particular theme might be quite rare or not exist at all. It also depends on the various fanfiction platforms and their content policies.
A prevalent theme is the exploration of their relationship. This can range from a deep platonic bond to something more romantic in some fanfictions. Also, the theme of loyalty is common. They are loyal to each other as members of their team, and fanfictions will often have situations where this loyalty is tested, like when one of them is in danger and the other has to make a choice to save them.
You can start by looking on Archive of Our Own (AO3). It has a large collection of fanfics, including many Ruby Weiss ones. Just use the search function and type in 'Ruby Weiss' and you'll get a bunch of results.
One reason could be Ruby's lack of respect for Weiss's family name or heritage. Maybe Ruby made a joke that Weiss found offensive about her family's reputation in the world of Remnant. So, Weiss yelled at her to show her dissatisfaction.
In a wolf - centered fanfic, Ruby Rose and Weiss Schnee might be on a mission related to wolves. For example, a pack of wolves has been acting strangely due to some dark magic. Ruby and Weiss have to figure out what's wrong. Ruby's enthusiasm and Weiss's determination would drive the plot forward as they work together to solve the mystery.