The "green" aspect of it is a reference to the green mushrooms of any super mario game that gives you "1-up". By definition, a greenie will always try to "1-up" whatever you've just said/done to conpensate for their own lack of self worth.
Zak: yeah, I solved world hunger.
Felicia: No you didn't. Be happy for her and stop being such a 1-Up'ing greenie s.o.b.!
Derived from Puzzle pirates were new players names are written in green.
Dude 2: What a greenie
Used in sports, the Army, etc. Also as a diet pill.
Also referred as "beans"