Let me explain.
We’re talking about federal immunity, which can be one-off (proffer letter), a deal between the government and a witness (letter), or judge-granted (statutory). These gents presumably received letter immunity, which means prosecutors decided what they had to say about Cohen was worth not using it against them. It’s a strong variety of immunity, sometimes called “blanket immunity.” But it has limits.
You’re granted immunity with respect to what you disclose—and only what you disclose. Neither your testimony nor evidence that derives from it can be used against you, but you can still be prosecuted for unrelated charges, things you said nothing about. An immunized witness can even still face related charges if prosecutors can build a case independent of the information a witness provided on the condition of immunity, though it’s an ethically dodgy move.
Weisselberg, as a longtime Trump loyalist and CFO of the Trump Organization, has almost endless potential to assist prosecutors investigating the organization and members of the Trump clan. That doesn’t mean that’s why prosecutors decided to grant immunity, that Weisselberg did more than confirm Cohen’s account, or that they’ll act on that information. (We can only