Picka-back or a-Pigger-back, does not mean as a pig is carried by a butcher, but as a piga or child is carried. It should be written apiggaback. A butcher carries a pig head downwards, with its legs over his shoulders; but a child is carried with its arms round your neck, and legs under your arms.
“She carries the other a pickapack upon her shoulders.” —L'Estrange.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894