The following is the transcription of a letter from Lot Davis (Judge of Probate Court 1888-1894) to J. A. Bowen. It gives a good description as to why the consents were needed.
(scroll down to view the actual letter)

OFFICE OF

THE PROBATE COURT,

LAWRENCE COUNTY,

Ironton, O, May 10, 1888

J. A. Bowen
Athalia

Dear Sir:        


Your favor of the 7.00 rec'd & contents note. I refer you to Sec. 6384 & following secs. of Rel Stat.
1. Before a license can be issued one of the parties must be present & subscribe to the oath as to age, relation, residence & whether either has husband or wife living and finally to swear that there are NO legally impediments in the way of their marriage.

2. If the parties or one of them are not here personally, someone must be who will subscribe to the oath. Or

3. If either of the parties are not of age the written consent of the parents, the writing witnessed by two parties, one of whom must come to town and in addition to the above oath make affidavit as to execution of consent of parents & that the said consent is on file in the Probate office.

I need not say to you that the law is tri?? in this particular nor that I am subject to a heavy fine for violating any of the provisions of Secs. above referred to, for this you already know. I would like to accommodate you but can not. I declared some time ago when one of our justices came very near getting me into trouble that I never again would take any chances. In that case the parties were not only minors but first cousins & the parents were bitterly opposed to the marriage. They live in your township. I return your money and hope all will be satisfactory.

Truly Yours        
Lot Davis