Christians began meeting on Sunday for several reasons: to set themselves apart from the Jews, the predominance of Gentile converts in the church in Rome, and Pagan sun worship, among other factors.
At first, the church is Jerusalem was the dominant church. After the destruction of the Jerusalem temple in AD 70 and the scattering of the Jerusalem Jews, including the Christian Jews, the church in Rome, comprised primarily of Gentiles, became the dominant church.
Sun worship also played a part. In order to help get more pagans to accept Christianity, it behooved the church to move services to a day when the Pagans were already used to worshipping - Sunday, the day of the sun.
Emperor Hadrian also played a part. He outlawed Sabbath keeping in 135, making it expedient to change the day of worship to avoid the persecution that the Jews were undergoing.
These reasons are covered in much more detail in Biblical Perspectives, Issue 64 (Seventh-day Adventist site), which is itself a short synopsis of the 350 page book From Sabbath To Sunday.
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