Remember that old children's game Telephone, where a word or phrase would be whispered whispered down the line until it got to the last person? In most cases, the resultant phrase sounded nothing like the original. Such is the case of "piggyback." It has nothing to do with an actual oinker, and everything to do with a misquoted phrase.
Experts believe the original phrase dates back to 1565 and was "pick-pack," meaning objects that were taken from storage and pitched onto a person's waiting shoulders for transport. As time went on, the phrase mutated to "pick-a-pack," and then to "pick-a-back," which ultimately turned into "piggyback."