I find Big Mama fascinating. And part of that is because I see her as a character who tries to give people what they want. Now, 'want' is a very important word here. She doesn't make people better, provide things that they need, she is deeply an enabler. A monkey's paws. Her design is based on a jorōgumo from Japanese folklore. A spider woman, who takes the guise of a beautiful woman to fool men, mostly to their doom. She ensnares or presents something and lets her prey walk into the web of their own volition. In the show, she is a crime boss that makes her money on gambling, auctions, and generally through the indulgence of the vices of others.
And I think this holds true in the dynamics of the show. Her romance with Lou Jitsu is classic bait and switch, but taking him to the Battle Nexus, making him her Champion? Despite the fact that we know he resented it, considered it kidnapping, that it was not good for him, we still see in flashbacks how much he loved the glory and attention of it. How much he still craves it. The siren song of 'glory' is tied to the Nexus, not to his film career. Actually fighting for his life, with real stakes and real applause is what he romanticizes.
Likewise with the Boys when they meet her. They are clearly young, alone, and in over their heads. So, Big Mama comes in soft, matronly, and with honest answers. Overloading them with information and praise, being 'vulnerable' by showing them her true form, and offering them help. An act that all, but the little manipulator himself Leo, fall for. But they still get the oozesquitoes. Because she's offering them what they want - guidance. No one had explained a single thing to them before Bug Busters. They didn't know the term Yokai, their solo plans to catch the oozesquitoes failed, their contact with yokai culture had been largely hostile and unwelcoming. Big Mama was the first Yokai to be nice and helpful. And even when she turned on them, as is her nature, she wasn't going to hurt them, just put them to work. (I have thoughts about why, but that's more fanfic territory)
And this is this mechanism which Leo uses to out play her in Many Unhappy Returns. She is so accustomed to dealing with overconfident men, to trapping them with their own hubris by simply saying 'yes' and indulging their desires that she doesn't see the trap being built around her. She doesn't see how petty this teenager is, how focused he is on need over want. His siblings are fighting for their lives, after all. And suddenly, Big Mama is in the position of wanting something. She is saying 'yes' not just to their wants, but to her own and it's just enough room for Leo to get what he needs. A way to stop the Dark Armor. But of course, Big Mama wouldn't be Big Mama if she didn't offer them an irresistable want she could then twist to her advantage, disposing of it.
Battle Nexus New York is purely a spiteful cartering to the worst kind of personal desires. I am sad this episode felt so rushed, but what we got is still telling. Raph and Mikey paired with their villain foils/personal idols. Customized challenges to play into each character's vanity. A chance for them to prove they are the funny/smart/strong/creative one. A chance at Glory, like their father, and heroism in saving New York. I tend to think Raph's clever move with The Hibernator changed her plans, whatever they may have been, forcing an escalation that was likely inevitable. At this point in the series, our dear boys are pretty aware of her tricks and that there is always a web waiting to ensnare when Big Mama is involved. Better to play your own game than hers. And it all comes unraveled.
I find Big Mama so interesting because she is alone among the Big Villains - Draxum, Shredder, and the Krang. (Sure, Sister Krang(or Krang 2) exists, but Krang is Krang.) Despite her truncated storyline. I could assume there was some tragedy planned for her story, based on the other villains we were given, but that was not really in the text. Unless you read her affection/obession with Lou Jitsu as genuine. But she is a powerhouse of a woman. A manipulator. A schemer in a way the other Rise Villains really could never or would never pull off. In a show full of city destroying monsters, she is terrifyingly civilized. And I realize that is a space normally reserved for Shredder in other iterations - the schemer and shadowy cabal leader - but I think there is something particularly great about Big Mama. She gets to live in this grey space, not quite on anyone's side, but her own. She can have fun, throw parties, go about her business, be confident, loud, and weird. Rarely, if ever raise her voice. Have loyal people that she clearly treats well, because all their wants are freely fulfilled. And still be scary.
Because a monkey's paw is always scary. The temptation to use it will always be there. You will always WANT something. And she will always be happy to provide.