In this paragraph we read of the good relationship and reception that Paul had with the church in Galatian when he first went to preach the gospel. He was sick during that time and they cared for him.
Some speculate that the weakness of the flesh is the same as the 'thorn of the flesh' in 2 Corinthians 12:7. This may be true. But we can't know for sure. What we can know for sure is that the Galatians are praised for receiving Paul as a messenger of Christ. This should be our attitude to his writings as we read them. They are the very words of God to us.
Galatians 4:12 Become as I am, for I also have become as you are. You have not wronged me;
13 you know that previously I preached the gospel to you because of a weakness of the flesh. 14 You did not despise or reject me though my physical condition was a trial for you. On the contrary, you received me as an angel of God, as Christ Jesus himself.