The image for the 1841 census in your sources shows William 2 years old, not 0 - perhaps twin with Robert? Father Robert is a manufacturer and there is a possible marriage 25 December 1837 at Manchester Collegiate church, now cathedral , Robert Pearson manufacturer of Hoghton, Lancashire, father Robert Pearson, farmer, Eloise Mercy Williams of Ardwick, father William Williams, bookseller. Pearson is a very common surname and the GRO has 134 William Pearsons registered 1838 - 1840 so I would look further down the tree as someone has suggested and find all the information you can about William and Robert junior.