I don’t think Weigel was telling the Pope how to be Catholic. He was engaging in a dialogue that the Church (including the Pope he was disagreeing with) says is necessary. Just War is an issue on which there can be differing opinions by faithful Catholics. And I don’t think Weigel said the Pope was wrong to oppose Bush; he said that he disagreed with the Pope’s conclusion.
There is a significant difference between saying the Pope is wrong to oppose Bush, and saying the Pope came to the wrong conclusion. The former says that the Pope has no right to oppose Bush. The latter says that he has a right to oppose Bush. It says something different: “I respect your right to criticize, but I reach a different conclusion as to the justness of the war.”
The Pope’s opposition is something that a faithful Catholic must listen carefully to, and give great weight to, and I am sure that Weigel, a faithful Catholic, gave it great weight. But giving it great weight doesn’t place it in the area of infallibility. Other issues which the Pope may not have addressed could lead to a different conclusion; so could disagreements as to various aspects of how the war might be fought, or how much emphasis to give on various aspects of the decision making process.
Rather than Weigel telling the Pope how to be Catholic, Weigel, along with the Pope, was being Catholic.