Etymology

Derived from sailing ships. The 'sheet' in the phrase uses the nautical meaning, of a rope that controls the trim of sail. A sheet that is in the wind has come loose from its mooring and is flapping in the wind like a flag. A sail (normally jib sails) is said to be sheeted to the wind, when it is set to backfill (set to the opposite side of the ship from normal use).

   A backfilled jib is normally a bad thing.  But in a major storm when a ship is “hove to,” the helm is lashed to windward, and the jib(s) are sheeted to the windward side of the ship (sheeted to the wind) causing the ship to sit sideways to the wind and waves to minimize the distance the ship is blown off course during a storm.  While hove to the ship is at the mercy of the wind and the crew has no control of the ship.
   As the storm gets stronger, more force is required to hold the ship in position and additional jibs are sheeted to the wind to keep the ship balanced.  A ship that has three jibs sheeted to the wind would be sitting sideways to the wind and waves in hurricane conditions, causing it roll wildly from side to side and in constant danger of rolling over with each wave.  
   Hence, a totally inebriated person is out of control and in danger of crashing, just like a ship three sheets to the wind.