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]