Vito Genovese wanted to take over the crime family led by Frank Costello. CrimeLibray.com said this: Moretti's Jersey boys also provided the muscle behind Costello, and eliminating Moretti would weaken Costello.

But why does the head of the Luciano(later Genovese)-family need a Willie Moretti who only has 50-60 buttonmen? The Genovese crime family was the most powereful (and largest?) crime Family in the US, so why needed Frank an ally? I mean Frank's family was far more powerfull than Moretti's..wasn't it?

By taking out Moretti you're taking out someone who will eventually come after you seeking revenge.

Juventus, as you probably know, Luca Brasi was partly modeled on Willie Moretti. Moretti, although short of stature, was truly "like a natural force," and was much feared. But unlike Luca, he didn't belong to one family--several NY families used his services. Supposedly, Moretti met the ship that brought young Joe Bonanno to America, and helped him get started.
Yes, killing Moretti did weaken Costello. But it's also a fact that Moretti, toward the end of his life, suffered from tertiary syphillis. His mind deteriorated, and he began blabbing about things he shouldn't have. Genovese did arrange for his assassination, but I think some or all of the other Mafia bigshots concurred.