Obviously, they must have something on him.
Supposedly, there was (under US law) an irregularity in the adoption of his children, who were born in Ireland but were adopted through a religious order in a Latin American country. There was nothing underhanded about it; it was a Catholic agency that was international.
But I think it may have conflicted with US law in some way, because US law is designed to discourage adoption and encourage abortion. So I think this is probably what was used.
However, Roberts gave Congress a way to kill the thing by declaring it a tax. If it’s a tax, it had to originate in the House. It didn’t, but was imposed through the Senate and the Executive. If someone challenged it on these grounds, which I think was what Roberts hoped, it could easily be defeated.