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Read it again, only rather than begin where James declare agreement with Peter.

It was quite clearly brought to all the Apostles and elders, and there was much debate.

Peter stands and gives testimony to the fact that the Holy Spirit revealed to him that the uncircumcised could receive God’s grace through Jesus.

James merely affirms what Peter has said and agrees that no burdens should be placed. It was James’ judgement that the burden of circumcision should not be place upon the Gentiles and all the others agreed with him.

James was not the “leader” nor was he the final authority.

Peter has the vision regarding Cornelius and his family.

Then....

1And certain men which came down from Judaea taught the brethren, and said, Except ye be circumcised after the manner of Moses, ye cannot be saved.

2When therefore Paul and Barnabas had no small dissension and disputation with them, they determined that Paul and Barnabas, and certain other of them, should go up to Jerusalem unto the apostles and elders about this question.

Then....

5But there rose up certain of the sect of the Pharisees which believed, saying, That it was needful to circumcise them, and to command them to keep the law of Moses.

6And the apostles and elders came together for to consider of this matter.

7And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe.

8And God, which knoweth the hearts, bare them witness, giving them the Holy Ghost, even as he did unto us;

9And put no difference between us and them, purifying their hearts by faith.

10Now therefore why tempt ye God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear?

11But we believe that through the grace of the LORD Jesus Christ we shall be saved, even as they.

Then....

13And after they had held their peace, James answered, saying, Men and brethren, hearken unto me:

14Simeon hath declared how God at the first did visit the Gentiles, to take out of them a people for his name.

15And to this agree the words of the prophets; as it is written,

16After this I will return, and will build again the tabernacle of David, which is fallen down; and I will build again the ruins thereof, and I will set it up:

17That the residue of men might seek after the Lord, and all the Gentiles, upon whom my name is called, saith the Lord, who doeth all these things.

18Known unto God are all his works from the beginning of the world.

19Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:

20But that we write unto them, that they abstain from pollutions of idols, and from fornication, and from things strangled, and from blood.

21For Moses of old time hath in every city them that preach him, being read in the synagogues every sabbath day.

22Then pleased it the apostles and elders with the whole church, to send chosen men of their own company to Antioch with Paul and Barnabas;

There is a very clear sequence of events.

There is a revelation
The revelation is told to the apostles and the elders, who debate it’s message and what it means for the faithful.
A belief or position is formulated.
That belief is agreed to by the whole of the apostles and elders.
A message is sent out to the believers regarding what was agreed to and how it pertains to the lives of the faithful.

This is the blueprint for all the following councils and synods and such that the Church has had since.

James agrees with Peter and clarifies what his judgement is on the subject of the debate.

Sentence:obsolete : opinion; especially : a conclusion given on request or reached after deliberation

James makes no pronouncement, he gives his opinion upon hearing all that Peter and the others say. And the others do not acquiesce to James, they agree with him and acquiesce to the revelation given to Peter.