And here's the 1880 census showing a Welthy Rogers, right age, with a sister Amelia, in Morrow, Ohio:
"United States Census, 1880," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:M8SW-3QH : 14 July 2016), Welthy Roggers in household of Henry Roggers, Westfield, Morrow, Ohio, United States; citing enumeration district ED 122, sheet 220B, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 1053; FHL microfilm 1,255,053.
But you still need to confirm that Amelia who married Weltha's widowed was the sister.