Slang, possibly from the end of World War II, but it was certainly used by the
US Army during the
Vietnam War. It means a heavy or awkward load in
adverse or difficult circumstances.
When they first heard it, the expression “humpin’ the pig” the word
humpin' caused a certain amount of consternation among reporters (see humping). The pig in question was not a pink bacon producer or an officer of the law but nickname for the
M60 machine gun, so the grunt they were interviewing would have been a
machine gunner.