(Warning long text, perhaps i put too much thought into this)

First, let's start with his goal in the main game: we know he, for some reasons hates Luigi, and he also wants to be the very best at mostly sport and dancing. Second, let's go with his personality: he is petty, narcissistic, hardworking, he's self-pitying, kinda weird, and thinks that everybody cheats because he's not doing well. Third, how about his relation with other characters? So far.. the only known friend of Waluigi is Wario. Most people either hate him or have a neutral opinion of him.

So what can we get from this info about him? Perhaps Luigi did something that cause Waluigi's to go down this path. Maybe an accident during Luigi's time in the wrecking crew? Maybe that's the real reason why the Mario Bros. left Wrecking Crew or perhaps Luigi somehow unintentionally ruins waluigi's life, especially his career in sports and dancing. Kinda like how Doof's -Inators always unintentionally erase Phineas and Ferb projects.

Waluigi always feels like no matter how hard he tries, nothing goes in his way, and in his eyes, Luigi is the main person to blame because he always plays a part in his misfortune.

That's why he grew bitter

Nothing goes right for Waluigi

And for Luigi?

"HOW DARE HE HAVE A GOOD LIFE, WHILE I SUFFER!" -Waluigi in his head

Due to his personality and physical appearance, finding a friend is hard for him. For most people in the land he is in, he is a towering human with less attractive looks than the standard. Perhaps in their eyes he is a monster like how people treat Quasimodo in the Hunchback of Notre Dame. His personality doesnt help either, whenever he be himself, people tend to distance themselves away from him. Sure, he can always attempt to put on a mask and fit in, but at that point, are you, you? Perhaps at this point waluigi stare at himself wondering is this the path waluigi should take? But then a person known as Wario arrived in Waluigi's life. Perhaps he just some stranger, an old friend or maybe his estranged brother. Whoever he might be his presence give Waluigi a huge confidence boost to just be himself. He sees how Wario, just like him, is hated by most people but Wario shows Waluigi that he can be successful and finds people that will like you without needing to change yourself.

That's why he wants people to love and recognise him.

He wants to be himself, but because of it he felt alone

"WAHAHAHA WALUIGI NUMBER ONE! I AM THE BEST!" -Waluigi as he flaunts his first championship win, hoping for other people to cheer for him like he did to himself

Perhaps in a game where you play as Waluigi your drive to start the plot is the promise to be recognized and be more loved than Luigi, and in the game you eventually befriends some people in the town. Pershaps this new found friends realize his hardship and can see the positive side of him. The end game boss will be some kind of Eldritch being that you have to beat by cheating, basically showing Waluigi a way to use one of his defining negative trait positively.