I believe this couple to be William Gage McIlhago/McIlhagga/McIlhaggie and Mary Houston who would have married about 1835 after the demise of Mary's first husband, William's older brother John. As I have suggested in earlier blogs, John probably fathered three known children, Henry, Eliza and William, Henry being named after his paternal grandfather. It is possible that William is the 'Willm' in Renfrew on the 1861 Census. However, to the best of our knowledge at present William was born in 1834 and 'Willm' in 1839, so they could well be two people. There is no reason why Mary could not have had two sons called William by different fathers, however 'inconvenient' it was to have step-brothers with the same name. And it appears that she also had two Henrys, for there are two half-siblings older than the four listed in Rutherglen in 1861, namely Rebecca (born 1836) and Henry (born probably in 1838).
The 1861 Rutherglen list has added the names of two children to my indexes, namely William and Mary. The fact of a Mary McIlhago living in Rutherglen in 1861 has opened up a further possibility. By 1863 she would have been twenty-two, and I have the record of a marriage on 6th June that year of a Mary McIlhage (an 'easy' variation) to a William Gibb. They had a daughter Mary on 22nd March 1867 in Belfast, indicating that between '63 and '67 they returned from Scotland to Ireland. However not all the family returned. By 1871 Mary senior (now McIllhago) aged 58 was living, apparently alone, in New Monkland and 'Willm', now 36, married to Catherine, 28, with four McIlhago children, were living in the centre of Glasgow.