1915, apparently from a language in the Philippines.
Registered as a trademark in Vancouver, Canada, in 1932, the year the first craze for them began (subsequent fads 1950s, 1970s, 1998).
Copyrighted by Donald F. Duncan in 1933 for the "Flores Yo-yo Company". This copyright moved to Papa's Toy Co. Ltd. when it bought out the former in 1965, but it was later determined that the trademark was improperly issued, so it's fine to use the word now.
The toy itself is much older and was earlier known as bandalore (1802), a word of obscure origin, "but it was from American contact in the Philippines that the first commercial development was established" [Century Dictionary].
Brought to the United States by Pedro Flores, who was born in the Philippines back when it was a U.S. territory. Thus, we can trace both the yo-yo and its name to the Filipino language of Llokano, where it was yoyo, with a special emphasis on the first o.
Figurative sense of any "up-and-down movement" is first recorded 1932.
Meaning "stupid person" is recorded from 1970.
The verb in the figurative sense is attested from 1967.