I found all of the following on Ancestry or FamilySearch; some of this information may help you:
This is the reference for an "Aaron Davis" son of Uriah and Reemah, this is from a typewritten transcript and the birthdates for the children in this record are transcribed incorrectly. This Aaron was probably born in 1792, not 1797:
Birth Date:25 Nov 1797
Baptism Date:16 Sep 1798
Baptism Place:Deerfield, Warren, Pennsylvania, USA
Organization Name:Presbyterian Church in Deerfield
Historical Society of Pennsylvania; Philadelphia, Pennsylvania; Historic Pennsylvania Church and Town Records; Reel: 127
The marriage record for Aaron and Ruth (Image available at FamilySearch):
Marriage Date:2 May 1816
Marriage Place:Washington, Ohio, USA
1850 U.S. Census:
Aaron P Davis
Birth Year:abt 1796
Home in 1850:Moscow, Muscatine, Iowa, USA
Aaron P Davis 54
Ruth Davis 53
James Davis 15
Maria Davis 11
Elisabeth A Davis 4
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MZ4N-6YR : 12 April 2016), Aaron P Davis, Moscow, Muscatine, Iowa, United States; citing family 19, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
Find-a-grave says Aaron was born in Wales, died and is buried in Washington County, Nebraska.
Aaron and Ruth are listed as the parents of James Davis on an 1888 marriage license issued in Washington, Nebraska.
There are numerous other tax and census records for "Aaron Davis" in Ohio between 1830 and 1850, but as you've noted it was a common name and it's difficult to know who was who.