There is a good chance the centrifugal clutch between the engine and the output shaft has come apart. Don't use it in that condition, you'll break the crankcase mounting or the plastic at the top of the shaft. Separate the powerhead from the shaft, remove the clutch housing, and take a look at the clutch.
If it's not the clutch it will probably be a failure of the shaft at the bevel gearbox at the bottom of the drive shaft. That usually causes loss of drive rather than unbalance though. If it is a slippage in the drive, focus on the gearbox. If it is a vibration up at the powerhead, but the drive is steady, focus on the clutch.
