There are many references in the book of Acts
about the early Christian church meeting
together on the Sabbath (Saturday) to pray and
study the Scriptures.
However, some Christians believe the early
church began meeting on Sundays soon after
Christ rose from the dead, in honor of the Lord’s
resurrection, which took place on a Sunday, or
the first day of the week. This verse has Paul
instructing the churches to meet together on the
first day of the week (Sunday) to give offerings:
And when Paul met with believers in Troas to
worship and celebrate communion, they gathered
on the first day of the week:
1 Corinthians 16:1-2
Now about the collection for God’s people: Do
what I told the Galatian churches to do. On the
first day of every week, each one of you should
set aside a sum of money in keeping with his
income, saving it up, so that when I come no
collections will have to be made.
(NIV)
Acts 20:7
On the first day of the week we came together to
break bread. Paul spoke to the people and,
because he intended to leave the next day, kept
on talking until midnight.
(NIV)
While some believe the transition from Saturday
to Sunday worship began right after the
resurrection, others see the change as a gradual
progression over the course of history.
Today, many Christian traditions believe Sunday
is the Christian Sabbath day. They base this
concept on verses like Mark 2:27-28 and Luke 6:5
where Jesus says he is “Lord even of the
Sabbath,” implying that he has the power to
change the Sabbath to a different day. Christian
groups that adhere to a Sunday Sabbath feel that
the Lord’s command was not specifically for the
seventh day, but rather, one day out of the
seven week days. By changing the Sabbath to
Sunday (what many refer to as “the Lord’s Day”),
or the day the Lord resurrected, they feel it
symbolically represents the acceptance of Christ
as Messiah, and his broadening blessing and
redemption from the Jews to the entire world.
Other traditions, such as Seventh-day Adventists,
still observe a Saturday Sabbath. Since honoring
the Sabbath was part of the original Ten
Commandments given by God, they believe it is a
permanent, binding command that should not be
changed.
Interestingly, Acts 2:46 tells us that from the
start, the church in Jerusalem met every day in
the temple courts and gathered to break bread
together in private homes.
So, perhaps a better question might be, are
Christians under obligation to observe a
designated Sabbath day? I believe we get a clear
answer to this question in the New Testament.
Let’s look at what the Bible says:
These verses in Romans 14 suggest that there is
personal freedom regarding the observance of
holy days:
In Colossians 2 Christians are instructed not to
judge or allow anyone to be their judge regarding
Sabbath days:
And in Galatians 4, Paul is concerned because
Christians are turning back like slaves to legalistic
observances of “special” days:
Drawing from these verses, I view this question of
the Sabbath similar to the tithe. As followers of
Christ, we are no longer under legalistic
obligation, for the requirements of the law were
fulfilled in Jesus Christ. Everything we have, and
every day we live, belongs to the Lord. At the
very minimum, and as much as we are able, we
happily give God the first tenth of our income, or
a tithe, because we know that everything we
have belongs to him. And not out of any forced
obligation, but joyfully, willingly, we set aside one
day each week to honor God, because every day
truly belongs to him!
Finally, as Romans 14 instructs, we should be
“fully convinced” that whichever day we choose is
the right day for us to set aside as a day of
worship. And as Colossians 2 warns, we should
not judge or allow anyone to judge us regarding
our choice.
Romans 14:5-6
In the same way, some think one day is more holy
than another day, while others think every day is
alike. You should each be fully convinced that
whichever day you choose is acceptable. Those
who worship the Lord on a special day do it to
honor him. Those who eat any kind of food do so
to honor the Lord, since they give thanks to God
before eating. And those who refuse to eat certain
foods also want to please the Lord and give
thanks to God.
(NLT)
Colossians 2:16-17
Therefore do not let anyone judge you by what
you eat or drink, or with regard to a religious
festival, a New Moon celebration or a Sabbath
day. These are a shadow of the things that were
to come; the reality, however, is found in Christ.
(NIV)
Galatians 4:8-10
So now that you know God (or should I say, now
that God knows you), why do you want to go
back again and become slaves once more to the
weak and useless spiritual principles of this world?
You are trying to earn favor with God by
observing certain days or months or seasons or
years.

http://dotwillis./2013/12/29/reason-why-christians-worship-on-sunday/