A yo-yo is a child's toy. It consists of a piece of twine, and two discs centrally joined with a spindle. The twine is attached to and wound round the spindle at one end, and to the child's finger at the other.
The trick is to make the yo-yo roll up and down the twine, and perform various gymnastics while so doing.
The image here is of the "back and forth" motion of the yo-yo. Thus Sharon's weight fluctuates violently. ("Yo-yoing" is the participial form of "to yo-yo".)