The OED has this explanation:
piggy-back, pick-a-back, advb. phr.
The primitive form was perhaps either a pick back or a pick pack; origin and form uncertain; the earliest examples have back, but the usual 17th century forms had pack, which still occurs in some dialects.
The evidence does not show whether the expression originally referred to a pack picked (pitched) on the back or shoulders, or to the back on which it is pitched; nor does it appear whether a pick answered to the French � pic �vertically, perpendicularly�, was due to reduplication as in tip-top, etc., or had some other source.