OK, so I got the Sorel Anglican Church vital records index, and it has given me a lot more information to work from. There are several Weightman/Whitman and See/Sea records. These are my new hypotheses given the new info:
It seems that two Weightman's (brothers?) settled in the Sorel region around the same time - John in Saint-Hugues and Hugh in Sainte-Anne-de-Sorel. John married Catherine See, and Hugh married Elizabeth Edvage, though neither marriage record is in the Sorel records.
John and Catherine had several illegitimate children, Hannah, Ann and John (who was baptized as an adult in 1858), though they appear to have married by 1831. Additionally, it seems that John was married previously to Catherine, as the Sorel records include a marriage of William Weightman, witnessed by his stepbrother John and stepmother Catherine Weightman. According to Hannah Weightman's baptism record in 1825, John Weightman was of Chabois or Cheboit, and Catherine See was of Pot au Beurre. I am unsure of where either of these places are supposed to be. John (Sr.) died Jun 27 1864 aged about 76. At this time his name was recorded as "Whitman."
Hugh and Elizabeth Weightman had three children baptized in Sorel - Elizabeth, Mary Jane, and Hugh. In addition to the records regarding the families of John and Hugh, it seems there was another Weightman. There is a baptism record for Elizabeth Weightman, born Sep 10 1819, "Daughter of Thomas and Mary Weightman, late from England." What does it mean by "late from England?" I assume it means they arrived fairly recently compared to the others.
Apparently, there were also three See's or Sea's (also brothers?) who settled around Sorel: James, John, and David.
James was a "former captain in the provincial militia, a native of New York state who came to Canada during the American revolution, died aged 81 and was buried Dec. 28, 1827, witnessed by David See." He was married to Mary, a native of Westchester, NY and resident of Sorel. They had sons David, Abraham, and John. David married Catherine and had William Henry, David, John James, Charles Henry, and Maria Ann. John was a merchant in Sorel.
John was an "American Loyalist late on the provision asylum of Sorel, died aged about 70 and was buried May 16, 1828, witnessed by David See." There was no other information on John.
Finally, the only records for David Sea were the baptisms of two of his children. He was married to a woman named Lenah or Leanah, and had Catharine, Apr 07, 1786, and Herman, Oct 28, 1788. This makes me think that this might be the Catherine who married John Whitman, and the same Catherine Whitman that J.J. pointed out on the 1881 census, as the date of birth would match exactly.
Anyway, I know this is a long post, but maybe it might help generate ideas about where to go next. I'm especially curious about what is meant by Cheboit and Pot au Beurre. I cannot find these locations, except for a road named Pot au Beurre in St-Michel-d'Yamaska, as well as a River near Ste-Famille I think. Please share any other pertinent thoughts you may have as well. I would also like to thank polarbear for pointing me in this direction, as I wouldn't have found any of this without your help.