In the context of verse 1, this “bearing a burden” may refer to a burden carried by the brother caught in sin. But the language could also refer to financial burdens. This is possible since the next paragraph deals with helping others financially. There is a great deal in this paragraph that indicates Paul has money in mind here, although it is not good to limit the “burdens” to only financial distress.
The warning in verse 3 is significant since it implies that the person who is not willing to help other believers carry their burden deceive themselves by thinking that they are “something.” Perhaps someone might think that they are too important to help the poorer members of the congregation. They may think that they are “above” that sort of thing. Paul’s preference in v. 5 is that everyone takes care of their own “load” (φορτίον, a word that can refer to cargo, Acts 27:10). This is similar to Paul’s teaching that people ought to work hard to provide for their needs (1 Thess 4:11-12, 2 Thess 3:12; Eph 4:28)
By bearing one another’s burdens, the believer “fulfills the Law of Christ” (v. 4). What is the Law of Christ?
One possibility is that the “Law of Christ” is at least a portion of the Mosaic Law, perhaps the moral aspects of the Law. It is hard to believe, however, that Paul would say that the Gentile believers in Galatia could do part of the Law by helping those who struggle with sin.
A second possibility is that this refers to the teachings of Jesus in the Gospels. This is attractive since Paul taught the churches in Galatia about the Life, death and resurrection of Jesus. But it is hard to point to a verse in the Gospels (which were written after Galatians), such as the greatest commandment (Matt 22:34-40) as “the Law of Christ.”
A third way to read this verse is that the “Law of Christ” stands in contrast to the Law of Moses. Romans 3:21-26 makes this point by contrasting the law of works (the Mosaic Law) with the righteousness obtained through the death of Jesus. In this view, the Law of Christ is equivalent to the New Covenant (1 Cor 11:23-26), the law of the Spirit (Rom 8:2), and walking by the Spirit (Gal 5:22-23).
Yet another way to look at the Law of Christ is to read it in the light of “bearing burdens.” Christ bore our since in his body, if we are to be like Christ then we should be ready to bear the burdens of others who are in Christ.
To “fulfill” (ἀναπληρόω) this Law is to carry out a responsibility or obligation. The word occasionally means “to complete a work” (Josephus, Ant. 8.58; TDNT 6:305). Members of the Galatian churches wanted to fulfill the Law of Moses, yet they could never actually keep the whole law, let alone “complete it.” Paul now tells them that they can fully complete the Law of Christ by bearing the burdens of their brothers and sisters.
As a general rule, Paul thinks that people ought to support themselves, but he also knows that there will always be people who cannot do so. Circumstances are such that they are unable to meet their obligations. In those cases a “mature spiritual community” will be “able to distinguish those loads which individuals must bear for themselves and those burdens where help is needed” (Dunn, Galatians, 326).