In the cartoons, Swee'pea was Olive Oyl's cousin.
FROM WHAT POD SPRANG SWEE'PEA?
Lil Swee'Pea, as Popeye likes to say, is an "adoptid infink." Historians of newspaper comics say he first appeared in his long nightshirt on July 28, 1933. The expressive babe appeared in his first cartoon short film in Max Fleischer's 1936 "Little Swee'Pea," in which Popeye blusters:
There's no ifs or maybes
I'll never has babies!
I'm Popeye The Sailor Man!
Popeye first appeared on Jan. 17, 1929, in the comic strip Thimble Theatre, which had already been drawn for 10 years by E.C. Segar.
The strip originally revolved around Olive Oyl's family. Her parents were Cole and Nana Oyl and she had a brother named Castor Oyl and a boyfriend, Ham Gravy. She was also — believe it or not — a tad pudgy in the beginning. (Too much Ham Gravy, no doubt.)
Popeye quickly eclipsed the other characters to become the star.
http://www.jewishworldreview.com/0905/glad_u_asked.php3?printer_friendly
In 1933, Popeye received a foundling baby in the mail, whom he adopted and named "Swee'Pea".
Swee' Pea (Popeye's "adopted" baby son in the comics, Olive's cousin in the cartoons)
https://en.wikipedia.org/wiki/Popeye