Something that you will eventually get and continue to get once you become a Marine. Getting the "big green weenie"
may include such fine events as: getting fucked with duty on a particularly important weekend, getting in trouble for some small petty shit while being in garrison, getting stationed at a shithole like 29 Dumps.
The "big" represents the big
bad Marine Corps picking on the little
guy, the Marine. The "
green" represents the true color of the Corps. The "weenie" represents getting fucked over.