The behavior of a person who has fallen asleep sitting up (as in a car on a long trip), where they will start to slump farther and father towards one side and then jerk back to an upright seated position, then repeat the cycle, all without ever waking up. Refers to the toy for small children called Weebles, marketed with the slogan "Weebles wobble but they won't fall down."
For five hours on our family road trip I had nothing to do except watch my sister sleep weebling.