I think I know, based on something I heard in a film some time...

• It was meant to be "a small pounding of pain"
• But through a typographical error it became "a 1/4 pounding of pain"
• And of course, in France, this became "a Royale with Cheese of pain" (due to the metric system).
• And finally this became "a cheeseburger of pain", (likely because of an undisclosed Copyright claim)

I can't back this up with any evidence, but it seems the most logical reason.