My records show that Alexander was b:1829 in Canonbie and d:1888 in Canonbie.
Son James b: 1853 Canonbie married Margaret Jackson b: 1856 Newcastleton, Rox. Their children were: Alexander (b:1875 Canonbie), Elizabeth (b:1877 Bewcastle, Cumbria), Walter (b:1880 Bewcastle), Jemima (b:1881 Bewcastle), John (b:1884 Bewcastle), and Phoebe (b:1886 Bewcastle). It seems odd that Alexander died in 1888 in Canonbie....I'd think it more likely he died in Bewcastle? Bewcastle records might be a useful study for you.
The only other child I have on record, born to Alexander and Jemima Tait is John Weir Little (b:1856 Canonbie, d:1894 Canonbie) married Mary Ann Dunn (b:1855 Kirkcudbright). One son Alexander (b:1882 Canonbie).
Relatively yours,
Merv