The word can be used to refer to such a spaz or retard who always
hogs the seesaw even if there is nobody on the other side. When a play-ground is over-run or especially renowned for the presence of retarded children it is said to be full of upty-downys. The word is derived from the simpleton way of explaining the motion of a seesaw.
Jim: Nah, you kidding? That place is full of upty-downys.
Ad: What would you like to do at the play-ground?
Olz (retarded): I want to sit on the upty-downy. <while dribbling> I love the upty-downy. Duhhhh.