I have a few questions and comments concerning the texts given as proof of Sunday worship outlined in the article: "Is sex on the Sabbath a sin?" The verses are Acts 20:7 and 1 Corinthians 16:1-2.
Acts 20:7 speaks of an act that is done on any day and nowhere does it say that the day is made holy simply by eating bread. I break bread Sunday through Saturday, but it does not make any of those days holy.
1 Corinthians 16:1-2 speaks about gathering offerings ahead of time so that no offerings would be made when Paul comes to Corinth. Also, the collections were to be made at each saint's house, not in church. So how can this be proof that we should worship on Sunday because these collections were not even made on Sunday, but throughout the week?
"Now on the first day of the week, when the disciples came together to break bread, Paul, ready to depart the next day, spoke to them and continued his message until midnight" (Acts 20:7).
The first day of the week, what we now call Sunday, is distinguished from all the other days of the week in this passage because this was the day the disciples came together to break bread. The phrase "break bread" refers to a meal, just as we use the word "supper" to refer to a meal. "Break bread" can refer to a common meal, or it can refer to the memorial meal established by the Lord. For example, in "The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?" (I Corinthians 10:16) this breaking of bread is clearly referring to the Lord's Supper. "For I received from the Lord that which I also delivered to you: that the Lord Jesus on the same night in which He was betrayed took bread; and when He had given thanks, He broke it and said, "Take, eat; this is My body which is broken for you; do this in remembrance of Me." In the same manner He also took the cup after supper, saying, "This cup is the new covenant in My blood. This do, as often as you drink it, in remembrance of Me." For as often as you eat this bread and drink this cup, you proclaim the Lord's death till He comes" (I Corinthians 11:23-26).
As you noted, if the breaking of bread referred to a common meal, then the distinction regarding the first day of the week as presented in Acts 20:7 is lost. Because this meal is distinct from all the meals the rest of the week, it becomes a clue that this is not a common meal.
Second, what distinguishes this meal is that it is partaken by the disciples. Common meals are eaten by every one, but this is a meal that disciples eat when they come together. When is it that they come together for this unique meal? They do it on the first day of the week. When Jesus established his memorial meal, the instructions were given to his disciples, thus again we see that this is a reference to the Lord's Supper and not a common meal.
Third, this meal was partaken when the disciples came together. The coming together of disciples is an assembly of the church. "For first of all, when you come together as a church ..." (I Corinthians 11:18). "Therefore if the whole church comes together in one place ..." (I Corinthians 14:23). One of the reasons Paul scolded the Corinthians was because they weren't coming together as a church in the proper manner to partake of the Lord's Supper. "Therefore when you come together in one place, it is not to eat the Lord's Supper" (I Corinthians 11:20).
Acts 20:7 doesn't talk about something that anyone does on any day of the week. Therefore, it is referring to the fact that Christians gathered on the first day of the week to partake of the Lord's Supper.
See also: "Is Acts 20:7 talking of a common meal?"
"Now concerning the collection for the saints, as I have given orders to the churches of Galatia, so you must do also: On the first day of the week let each one of you lay something aside, storing up as he may prosper, that there be no collections when I come" (I Corinthians 16:1-2).
The command was given to churches -- collections of Christians in a locale. This was not something individuals did independently. It was a collective action. Since Paul specifies a single day of the week on which this command was to be accomplished (the opposite of what you claimed), it is not as you argued, something a person does any or every day of the week. The command makes it distinct from my personal savings.
Each member of the church is to lay something aside, to store up what he prospers. Thus what is given is from the individual, but, since the command is given to churches, the storage is by the churches. Such is further emphasized by Paul stating it was so no collection needed to be done when he comes. If it was each individual savings, as you argued, then when Paul came those individual savings would need to be collected together -- the very opposite of what Paul commanded.
Thus once again, we see an action being done on the first day of the week by the church. And it makes perfect sense. The church comes together for worship. From Acts 20:7 we know that the Lord's Supper was done on the first day of the week. From I Corinthians 16:2 we know that giving was done on the first day of the week. So when did the church gather for worship? Clearly the day distinct from all other days is the first day of the week.