I know I'm late to the discussion but I skimmed over this thread and didn't really see this being brought up. But I think the concept of what "The Heavy" means as a real world term has been misunderstood.
For one, the term is a little more meta than what is being discussed as it is used by actors regarding playing the role of the villain. "Playing the heavy" means "are you ready for people to hate you for being the bad guy."
As a trope the closest analog I can think of is that some stories require someone to play the bad guy (or at least Devils Advocate) but they don't have to be the driving villain of the entire story. They offer the necessary conflict to get the story going but the story isn't about defeating the villain. For example all three Toy Story
films have characters who offer the danger and immediate conflict (Sid, Stinky Pete and Lotso) but the real threat (replaced by a newer toy, fear of being discarded when broken, no longer being played with) is something they don't have much to do with.
Now they certainly CAN be the driving villain of the plot as it is an open-ended term but the point is that they personify the conflict more than being responsible for it.