Oh right yes, he;s living in Middlesborough with his father Charles and mother Jane in 1881, but they were born York, his younger siblings were all born in Middlkesborough tho, they must have moved there when Joseph was about 2. is his Mother's maiden name French BTW???
He also had a Sister Jane A, too , 6 years younger than him, maybe she was the witness.
I can't find a close match to the details you have for a Mary Elizabeth Richardson born 1872 with a father George other than a Mary Eliza with father George born Liverpool.