First, the death date given by the Sweetser manuscript is not shown in Paxton records (should be here - be sure to use the date of death column, not the date of registration). Then there is a death, on the following page, of Elizabeth Sweetser in Dec 1853 (i.e., not 1852), but this appears to be William's mother since she is age 82. All this suggests some likelihood that the report of Eliza's death is based on confusion with her mother-in-law's death.
Eliza is listed of Warwick, and William's brother Samuel m. an Abigail Wheaton, d/o Abijah and Abigail Wheaton of Warwick. But no records are found for this family. So we cannot confirm her membership in this family.
Allred has no identification of Eliza, has no information on Abijah Wheaton of Warwick, but does show a Samuel Wheaton, s/o Reuben Wheaton and Abigail Partridge. If Eliza's middle name was Partridge (her initial of P is seen a lot but Partridge is only explicitly given in Sweetser manuscript), it would suggest she was Samuel's sister. But again no record is found.
The one clue we get is from the 1850 census (line 18) which shows her living in Worcester with her sons. Her birth is about 1810 in Vermont. She is an excellent match to the marriage record of Charles W Brown to Eliza P Sweetser found in Worcester in 1851 (record 50) but no birthplace or parents are given. If this marriage is true, she died before 1854 (but the Sweetser manuscript still appears to be reporting the wrong death) when this Charles W. Brown of Winchester married yet again (here).