After 70 years of being a father figure, Popeye officially adopted Swee'pea in a Sunday strip from November 21, 2004 in celebration of National Adoption Month. This was also marked by a special event held in New York City.
In the Plunder Island story arc, Popeye is fighting Alice the Goon when a little goon runs up and shouts "Mama!" Popeye is blown away to learn that Alice has a kid. He immediately stops the fight and promises to free Alice from the Sea Witch, so the two can go back to their home.
Early in the film we see Popeye keeps a picture frame with the words Me Poppa in place of a picture. The CMOH comes later when we see Pappy has an identical picture frame with the words Me Son.
Pick a Popeye/Swee'pea moment. Any Popeye/Swee'pea moment.
During the Sail With Me/Stay With Me song, Olive and Popeye sing about the futures they hope Swee'pea will have. There's a part where Olive is singing about how Popeye might be the guy she's been dreaming of, and that she hopes that he'll settle down with her.
There's also "He Needs Me", where Olive sings about how Popeye is the first person who's ever needed her.