The marriage record I found has the parents reversed from what you show.
Robert's parens: William and Alice and Ann's parents as James and Elizabeth.
Ontario, Canada Marriages, 1801-1928 about Robert Maxwell Name: Robert Maxwell Birth Place: Ireland Residence: Galway Age: 22 Estimated Birth Year: abt 1841 Father Name: William Mother Name: Alice Spouse Name: Ann Jane Weir Spouse's Age: 26 Spouse Birth Place: Ireland Spouse Residence: Minden Spouse Father Name: James Spouse Mother Name: Elizabeth Marriage Date: 24 Nov 1863 Marriage County or District: Peterborough
So I went to the 1861 census to see if they were with parents to confirm those names.
1861 GALWAY, PETERBOROUGH, CANADA WEST MAXWELL William, age 42, ship carpenter, born Ireland
Alice, age 45, born Ireland
Robert, age 19, labourer, born Upper Canada
John, age 17, labourer, born Upper Canada
Eliza,a ge 15, born Upper Canada
Alice, age 11, born Upper Canada
William, age 9, born Upper Canada
all are Church of England
I didn't find Ann Jane in 1861 census.
I see that in marriage both are shown born Ireland but 1861 Robert shown born ON and also in 1871 where both are shown born ON. Also in marriage Robert is shown born about 1841 and Ann Jane about 1837 but in 1871 he is born about 1842 and she about 1851 so something is off somewhere.
1871 GALWAY, PETERBOROUGH NORTH, ON MAXWELL Robert, age 29, farmer, born ON
Jane, age 20, born ON
HUNTER James, age 8, born ON
** I just noticed something - this couple are shown as married within the previous year with month of marriage shown as Dec. So is this a second marriage for Robert?? If so, what happened to Ann Jane - did not find a death for her but the database starts in 1869.
I found a death for Robert - 1882
Ontario, Canada, Deaths, 1869-1938 and Deaths Overseas, 1939-1947 about Robert Maxwell Name: Robert Maxwell Death Date: 3 Jan 1882 Death County or District: Victoria Age: 41 Gender: Male Estimated Birth Year: abt 1841
** he was a farmer, married, informant was Mrs. Maxwell of Galway
1881 GALWAY & CAVENDISH, PETERBOROUGH EAST, ON MAXWELL Robert, age 36, farmer born ON
Martha Jane, age 29, born ON
No children so if this is the same Robert as married to Ann Jane, he must have married twice and she must have died before 1869 (when death database starts.)
There is a family tree on ancestry which shows Robert born ON with parents William M. Maxwell 1819-1896, and Alice Lavery 1814-1877
They show marriage to Ann Jane Weir but no more for her - no census info for either of them , but they do show death same as I found.
I'm sorry I couldn't find Anne Jane with parents or anything more on her and Robert.