I found Gilbert Z. Avery in the Wood County, Ohio census as follows:
Gilbert Z. Avery 33
Eliza J. 26
Washington E. 5
John B. 3
Fanny M. 7
Jonas Zimmer 23
William R. H. Avery 23 (brother) (Also enumerated with father’s household in 1850)
Gilbert Z. Avery household, 1850 U.S. census, Wood County, Ohio, population schedule, Plain township, district 154, page 312, dwelling 687, family 709; National Archives micropublication M432, roll 741. [Ancestry Link]
Both my mother’s side and my father’s side of my family tree intersect about 4 or 5 generations back. It all comes down to the Averys and the Meekers of Wood County. Specifically the Averys descended from William Rufus Hyde Avery of New York and the Meekers descended from Mahlon Meeker from Sussex County, New Jersey. Many thanks to Darlene Lewis of Ohio for some of the information here and her research assistance.
Also, I will explore the inter-relation of the Averys to the Meekers of Wood County. It seems that many Avery siblings married Meeker siblings since the families lived next door to each other. I would like to track that and gain a better understanding of their relationships.