@Murcielago:
Pekoms said Bege was underestimating Mama. It makes clear that Bege is against Mama. But what makes him so self-confident ? I mean she's yonkou - one of the most powerful pirates in the world.
Someone like Capone would plan to take her down by strategy. I'm quoting Mr. 3: "If you know how to adapt your strategy, you can defeat anything" (chapter 118).
This is most certainly how he is planning to proceed. Betraying her at the right moment, when she's expecting it the least. @Murcielago:
Maybe it's "who makes him so self-confident" ? But there's no one nearby who can help him to deal with yonkou. Vinsmoke turned out being weak.
The G66 is… weak? Why? I'm guessing you're assuming this from the very-short-clash that opposed Judge to Sanji. You don't infer an organization's strength from this
Other than this, the Vinsmoke have nothing to gain from attacking Big Mom. It's quite the opposite; Judge needs her to get his hands around North Blue.