I grew up reading the King James Version. I don't use it much today though I still think it's an excellent translation. I can recall reading this passage when I was a teenager.
Note the underlined words. I was confused. If we are to bear one another's burdens, then why am I asked to bear my own burden? But anyone who knows the Greek here realizes there's no contradiction. Paul uses two different words for "burden." In verse 2 the word is barē; in verse 5 the word is phortion. The former usually referred to a heavy weight or load, whereas the latter word was the common term for a person's "pack." Hence there are two kinds of burdens in life. There is a burden that is too heavy for one person to carry. There is also a burden we cannot and should not share with others. When you go hiking, for example, you carry a pack that is light enough for you to carry by yourself.
By analogy, this applies to those responsibilities in life that are ours and ours alone. I can't carry your pack, and you can't carry mine. Hence verse 5 is better rendered "Each man will have to bear his own load." That said, we are also responsible to bear another's "burdens" since these burdens are too heavy for that person to bear alone. Such burdens must be carried jointly. Paul doesn't tell us what kinds of burdens he has in mind here. In light of verse 1, which refers to a Christian who has been tripped up by sin, Hendriksen thinks that the primary application "is the duty to extend help to the [fallen] brother so that he may overcome his spiritual weaknesses" (Galatians, pp. 232-233). This may well be the case. And note: the existence of pastor-elders in a congregation does not relieve members of their responsibilities to care for one another. On the contrary, all believers are to "admonish," "encourage," and "help" one another (see 1 Thess. 5:14).
What about it? There's something both touching and, well, very human about Paul's instruction here. You get the idea that personal relationships meant something special to him. Unfortunately, we forget that each of us -- you, me, your spouse, your mom and dad, your pastor -- is in desperate daily need of a Savior, not to mention a good, old-fashioned friend to encourage us, talk about things that matter, help build our faith, and explore with us the darker side of our souls.
In this regard, things really haven't changed much since Paul wrote to the Galatians two thousand years ago.