WMG / Luisa Miller

In the backstory, the previous Count had set his sights on Luisa

It's spelled out that the previous Count Walter was murdered by his cousin and his steward. The cousin's motive is clear as day, as it is an Inheritance Murder. However, the fact that Wurm instigated the crime rather clashes with what we know about Wurm's character: he is an utter Dirty Coward who is panically afraid of standing up to anyone more powerful than himself, so he must have had some serious reasons for risking his life and limb and committing a capital offence. He wasn't mistreated by the previous count: he recalls that the latter trusted him completely.

But there is one interesting detail Wurm mentions: his previous lord revealed his marriage plans to him because he trusted him so much. Why hadn't the late Count Walter told anyone else about these plans? Surely marriage isn't a shocking thing in itself... unless, that is, it's something scandalous, such as an Interclass Romance. Rodolfo is later perfectly ready to marry Luisa, so it wouldn't be that much of a stretch to suggest that the tendency to disregard the social norms of the time runs in the family. What if the previous Count, too, had taken a liking to Luisa Miller?

If there is anything else important to Wurm besides his own safety, it's his pursuit of Luisa (as he has spent at least a year trying to marry her, it's hardly a passing infatuation). He could very well assume that between him and the Count, Miller will choose the latter as his daughter's husband (we can see that Wurm has chronic problems with understanding that Miller simply wants Luisa to follow her heart), and so he decided to Murder the Hypotenuse before that could happen.

In the backstory, Wurm and Luisa had a brief romance before she saw his true colors

Wurm seems awfully confident that Luisa might one day genuinely soften towards him, as evidenced by his "comforting" words to her in their Act II scene ("Have courage, time is the medicine for any human grief"). Meanwhile, Rodolfo is awfully quick to believe Luisa's letter where she states she has always loved Wurm and only strayed towards Rodolfo out of ambition.

All of this would be far less ludicrous if we assume there is a grain of truth in the letter: Wurm and Luisa were once in a relationship. She is a trusting, impressionable girl, and he can put on a nice facade, as evidenced by the trust the previous count had in him. Perhaps, when he asked Miller for Luisa's hand, Miller told him to win her affections first, and Wurm briefly succeeded and courted Luisa for a while. As he is Faux Affably Evil, however, it didn't last long before his real nature showed itself in some way and Luisa broke it off. But Wurm remembers she used to have feelings towards him and thinks (wrongly) that she will love him again if only that pesky affair with Rodolfo is stopped, and Rodolfo knows about Wurm's history with Luisa (quite probably from Luisa herself). This way, the love letter, composed by Wurm, written down by Luisa and immediately believed by Rodolfo, is a much less random and much cleverer fake than it seems at first.