That ye submit yourselves ... - The word used here means evidently that you would show them proper deference and regard; that you would treat them with distinguished respect and honor for what they have done.

And to everyone that helpeth with us ... - Everyone who aids us in the ministry, or provides for our needs, etc. It is possible that Stephanas lived among them at this time (Note, 1 Corinthians 1:16), though he had been converted in Achaia; and it is probable that, as Corinth was a central place and a thoroughfare, others might come among them who were the personal friends of Paul, and who had aided him in the ministry. Towards all such he bespeaks their kind, and tender, and respectful regards.

1 Corinthians 16:16 Parallel Commentaries

The Apostolic Scriptures.
"And I think that I also have the Spirit of God."--1 Cor. vii. 40. We have seen that the apostolate has an extraordinary significance and occupies a unique position. This position is twofold, viz., temporary, with reference to the founding of the first churches, and permanent, with regard to the churches of all ages. The first must necessarily be temporary, for what was then accomplished can not be repeated. A tree can be planted only once; an organism can be born only once; the planting or founding …
Abraham Kuyper—The Work of the Holy Spirit

Jeremiah, a Lesson for the Disappointed.
"Be not afraid of their faces: for I am with thee to deliver thee, saith the Lord."--Jeremiah i. 8. The Prophets were ever ungratefully treated by the Israelites, they were resisted, their warnings neglected, their good services forgotten. But there was this difference between the earlier and the later Prophets; the earlier lived and died in honour among their people,--in outward honour; though hated and thwarted by the wicked, they were exalted to high places, and ruled in the congregation. …
John Henry Newman—Parochial and Plain Sermons, Vol. VIII

Ten Reasons Demonstrating the Commandment of the Sabbath to be Moral.
1. Because all the reasons of this commandment are moral and perpetual; and God has bound us to the obedience of this commandment with more forcible reasons than to any of the rest--First, because he foresaw that irreligious men would either more carelessly neglect, or more boldly break this commandment than any other; secondly, because that in the practice of this commandment the keeping of all the other consists; which makes God so often complain that all his worship is neglected or overthrown, …
Lewis Bayly—The Practice of Piety