Hello Sandyjose
Are they the couple in 1861 at RG 9/3266 Fol. 54 Page 13 at Fartown, Huddersfield?
Bradford Road,
Edmond Wear / Edmund Wear, H, Marr, 29, Carter, Birthplace Halifax
Eliza Wear, Wife, Marr, 35, Doncaster
2 Sons.
A search - Fartown Nonconformist - returns significant Nonconformism ...
Huddersfield Exposed
Category: Churches and places of worship
"
Purple represents Anglican places of worship, green shows Baptist places of worship, red indicates Wesleyan/Methodist places of worship, and orange represents other places of worship (e.g. Independent, Quaker, Roman Catholic, Swedenborgian, Unitarian, etc) or mortuary chapels."
https://huddersfield.exposed/wiki/Category:Churches_and_places_of_worshipSome Nonconformist (NC) Burials not online are with Chapels their HQ, Land/Building owners, Record Offices, Universities and elsewhere.
Also in Yorkshire about 6 General Cemetery Company cemeteries, first starting about the 1830s.
Many C of E Churchyards were closed from circa 1850s, so Local Burial Boards (some later became Council Cemeteries ) also began in Great Britain.
Marriage Amended
Suggestion online the 1855 WEAR = SHAW Marriage was at a Registry Office and might suggest one or both were not C of E.
Mark