I think she drowned crossing the Atlantic. He was certainly close to her, and it is said that he was never the same man again.
Yes--Theodosia met a tragic end in the Atlantic going from South Carolina to NY (from a geneology web site):
BURR, Theodosia [1783-1813]
Daughter of U.S. Vice President Aaron Burr. She is remembered for her devoted support of her father.
Hers is a tragic story: Following her 1801 marriage to Joseph Alston, scion of a prominent South Carolina family, Theodosia became chronically ill. She lost her 10-year-old son to malaria and was traveling to New York to visit her father when her ship was lost at sea. It is said that her ghost still walks their plantation.