There are a lot of thoughts that are circulated as to the answer to this question. I cannot answer for anyone else as to their motivation behind when they worship, but I can answer for myself and why I worship on Sunday. For me, it has nothing to do with the proclamation made by the Emperor Constantine I of Rome on March 7, 321AD. For me, it has everything to do with the resurrection of Jesus Christ. Some would like to say that we do not know if He really rose from the grave on Sunday or not, but for me Mark 16:9 is clear enough to settle that matter. God has Mark record in Holy Scripture, “Now when Jesus was risen on the first day of the week,” I believe He rose on that day not that He was risen before that day. Jesus made it clear He would be in the grave three days and three nights just as Jonah was in the whale’s belly in Matthew 12:40. In Mark 8:31, Jesus declared that he would suffer and be killed, and after three days He would rise again. It was also the first day of the week, the same day that He rose from the grave, that He revealed Himself to several of His followers in His glorified, resurrected form—first to Mary Magdalene in the garden, then later that day to two disciples as they traveled to Emmaus. This is recorded in Luke 24:13-35, two disciples clearly state that day was the third day since he had been crucified in verse 21. Then later that day, he reveled himself to the rest of His disciples, other than Thomas who was not gathered with them at that time. All of this happened on the first day. In the book of Acts, we see the disciples gather together for worship with preaching, fellowship, and remembering the sacrifice of Christ for their sins. In verse 7, it tells us this first century gathering of believers for Christian worship was on the first day of the week. And then in I Corinthians 16, we see instructions given to believers in church gatherings to receive a love offering in their worship service collections to aid other believers going through severe needs in Jerusalem, and this giving in worship in their cooperate assembly was on the first day of the week. All of this makes it clear to me that Sunday, although not the Sabbath, is the right day to worship for the New Testament believer in Jesus Christ as personal Saviour in celebration of our risen Saviour whose resurrection offers us victory over sin, death, and the grave as well as eternal life in Christ.