Is there any biblical support for Sunday observance?

You are perhaps aware that circumcision was a huge issue during the apostolic era of the first century. Conservative Jewish Christians insisted that Gentiles who wanted to become Christians should be circumcised first (well, the men at least!) and observe the other Jewish ceremonial laws. In other words, in order to be a Christian, a Gentile would first have to become a Jew. Then he could be a Christian. Paul said No. He insisted that Gentiles can come to Christ and be Christians directly, without having to go through Judaism (see for example Romans 3:25-29; 1 Corinthians 7:19; Galatians 2:12; 5:6-15; Ephesians 2:11; Titus 1:10). Therefore, Gentiles did not have to be circumcised in order to become Christians. Keep in mind that Sabbath was just as important to Jews as circumcision, and probably even more so. Thus, had Paul or any other apostle taught that the Sabbath was changed to the first day of the week, they would have raised a storm of protest from these conservative Jewish Christians, and this would have been just as evident in the New Testament as the controversy over circumcision.

The total absence of any such controversy over a change in the day of worship is one of the best evidences that the apostles and other New Testament Christians did not change the day. In fact, we have a record of many Sabbaths that Paul and his traveling companions kept. You can read about them in Acts 13:14, 27, 42-44; 15:21; 16:13; 17:2; 18:4. Acts 13:42-44 is especially significant. Paul and Barnabas had been invited to speak at a Jewish synagogue, and the Bible says that when the service was over, "the people invited them to speak further about these things on the next Sabbath." This would have been a great opportunity, had Paul believed that the Sabbath had been changed to Sunday, for him to tell the people to meet with him the next day rather than waiting a whole week. But the Bible says that "on the next Sabbath almost the whole city gathered to hear the word of the Lord."