6:2 The law of Christ referred to here is probably the summation of the law: "Love your neighbor" (see 5:14; Matt 22:39; John 13:34, 35). The term fulfill suggests that choosing to bear another Christian's burdens (or restore another Christian from burdensome sin, v. 1) is precisely what Christ expects of all believers. The Greek word for burdens refers to something beyond the normal capacity to carry, as opposed to a "load" (v. 5), which is what a person could be expected to carry.
[THE NKJV STUDY BIBLE Second Edition].
JESUS IS LORD.