As a teenage member of the Christian Church in Milwaukie I learned the answer to the question of why have the Lord's Supper every Sunday and for a long time, if anyone asked, I simply told them that we wanted to be a New Testament Church and this was the practice of the church from the beginning as seen in the New Testament. I had been taught that the Christian Church (along with the Christian Church (Disciples) and the Church of Christ) originated from a movement in the early 19Th century that wanted to restore the purity and simplicity of the N. T. Church. In fact, it was known as the Restoration Movement.
It was also a movement for unity. Thomas Campbell, one of the founders, described the divisions of the church in his day as a sword in the Body of Christ, rending and mangling it into a thousand pieces. He and others believed that restoring the essential practices of the N.T. Church was the means by which unity could be achieved. We can only have unity by giving up our special traditions and going back to the original church -- the church God intended and as revealed in the New Testament. It's a little like arriving at the correct time of day. If we all have different times we could add them together and take the average, or we could arbitrarily take the time of one of us, but we wouldn't necessarily have the right time. We have to go to the authority, the standard.
This kind of thinking led the founders of the Christian Churches to embrace a slogan: In essentials, unity, in opinions liberty, and in all things love. But what is essential to being the church? This may be debated but there is widespread agreement that the ordinances of baptism and the Lord's Supper are essential to the church. After all, they were ordained by Christ, hence the term "ordinances."
But how are they to be observed? The Roman Catholic Church has observed the Lord's Supper, the Mass, on a weekly basis for its entire history. But as the centuries passed the Mass became burdened with many traditions and concepts that took it far away from the simplicity and purity of the N.T. Church. Consequently, the Protestant Reformation tried to reform the practice of the Lord's Supper. Even though leaders like Martin Luther, John Calvin and others recognized the New Testament practice of weekly communion, and openly said so, the churches that resulted from their work adopted a variety of practices. Some observed it monthly, some quarterly, and some even less often.
It was in this context that Thomas and Alexander Campbell, Barton Stone, and others in the early 19Th Century Restoration Movement, led the Christian Churches to practice weekly communion. They believed that restoring the practice of the N.T. Church would help promote unity. As a result, we have the Lord's Supper weekly in our church. We want to be a biblical church, a N.T. Church, and follow what we believe is the Lord's will. At the heart of this, of course, is the fact that Jesus ordained it. In the upper room he took the actions and spoke the words that instituted the Lord's Supper.
Having said this I need to add one more thing. While I think what I have said is valid I also feel that the reason given above for weekly communion is inadequate. There is a deeper question that must be answered -- next time.