After all his polemics against nomos in Galatians, 6:2 comes as a shock: “So fulfill the nomos of Christ.” Paul plays similar tricks with the word elsewhere (Romans 3:27; 8:2; 1 Corinthians 9:21). Paul wants the Galatians “under law,” provided it is the law of Christ. (Note too Paul’s sudden shift into reverse at 5:6; after polemics against “works,” he says that the only thing that matters is faith “working” through love.)
Commentators have suggested various interpretations of “law of Christ”: The Sermon on the Mount as a Christianized Torah; or simply “love.” Some have thought the phrase must come from Paul’s opponents. But that simply misses the joke.
The first part of the verse, I think, defines what he means. It is right to say that the law of Christ is love, but in Galatians 6 Paul has something more specific in mind. ”Bear one another’s burdens” is the law of Christ because it involves doing for others what Jesus has done for us. Prior to that, in verse 1, Paul has urged the mature to restore brothers who go wandering. That is one form of “bearing burdens,” and one form that the law of Christ might take.
And that means that the law of Christ not only calls for patience and assistance to others. The law of Christ requires humble correction. It’s not for nothing that Paul speaks of nomos.