It seems Constantine had a role to play in it. Constantine is known for being first Christian Roman Emperor. However history tells us there was a mix of sun worshipping going on as well.
Sol Invictus ("Unconquered Sun") was a Roman god identified in the later Roman empire[ambiguous] with Sol, accompanied with the epithet invictus meaning unconquered that was commonly given to Sol from the second century CE onwards.
Emperors portrayed Sol Invictus on their official coinage, with a wide range of legends, only a few of which incorporated the epithet invictus, such as the legend SOLI INVICTO COMITI, claiming the Unconquered Sun as a companion to the Emperor, used with particular frequency by Constantine. Statuettes of Sol Invictus, carried by the standard-bearers, appear in three places in reliefs on the Arch of Constantine. Constantine's official coinage continues to bear images of Sol until 325/6. A solidus of Constantine as well as a gold medallion from his reign depict the Emperor's bust in profile twinned ("jugate") with Sol Invictus, with the legend INVICTUS CONSTANTINUS
Constantine decreed (March 7, 321) dies Solis—day of the sun, "Sunday"—as the Roman day of rest [CJ3.12.2]:
“On the venerable day of the Sun let the magistrates and people residing in cities rest, and let all workshops be closed. In the country however persons engaged in agriculture may freely and lawfully continue their pursuits because it often happens that another day is not suitable for grain-sowing or vine planting; lest by neglecting the proper moment for such operations the bounty of heaven should be lost.”
What about the early church and Sabbath:
Both Days Observed.
One thing is clear: The weekly Christian Sunday--whenever it did arise--did not at first generally become a substitute for the Bible seventh-day Sabbath, Saturday; for both Saturday and Sunday were widely kept side by side for several centuries in early Christian history. Socrates Scholasticus, a church historian of the fifth century A.D., wrote, "For although almost all churches throughout the world celebrate the sacred mysteries [the Lord's Supper] on the sabbath of every week, yet the Christians of Alexandria and at Rome, on account of some ancient tradition, have ceased to do this." And Sozomen, a contemporary of Socrates, wrote, "The people of Constantinople, and almost everywhere, assemble together on the Sabbath, as well as on the first day of the week, which custom is never observed at Rome or at Alexandria." Thus, "almost everywhere" throughout Christendom, except in Rome and Alexandria, there were Christian worship services on both Saturday and Sunday as late as the fifth century. A number of other sources from the third to the fifth centuries also depict Christian observance of both Saturday and Sunday. For example, the Apostolic Constitutions, compiled in the fourth century, furnished instruction to "keep the Sabbath [Saturday], and the Lord's day [Sunday] festival; because the former is the memorial of the creation, and the latter of the resurrection." "Let the slaves work five days; but on the Sabbath-day [Saturday] and the Lord's day [Sunday] let them have leisure to go to church for instruction in piety."
OK, I'm not an expert on this by any stretch. These are just some quotes from my google research for the day. But I'll try to summarize what I've gleaned.
- It appears the early church had a custom of gathering together on the Sabbath (7th day)
- They also celebrated Christ's resurrection on Sunday (1st day)
- Constantine's degree made Sunday the official day for the Roman Empire.
- The reasons for the church in Rome switching to Sunday may have had more to do with 'Sun' worship than 'Son' worship.
- I imagine within a few generations of Constantine's decree Sunday gatherings became the norm.
So it may not make much of a difference if we gather on Saturday, Sunday, or whenever.... as long as we gather, remember, celebrate and encourage one another.