* Itty: This is a diminutive form of "it," meaning "very small." It was likely formed by adding the suffix "-y" to "it," which is a common way to create diminutives in English (e.g., doggy, kitty, etc.).
* Bitty: This is a diminutive form of "bit," which also means "small" or "a small amount." Again, the "-y" suffix is used to indicate smallness.
Therefore, "itty bitty" is a double diminutive, emphasizing the extreme smallness of something.
While the precise origin of the phrase is difficult to pinpoint, it is likely to have originated in the late 19th or early 20th century in American English. It gained popularity in the 1930s and 1940s through its use in children's literature and songs.