Tony's big size as part of his boss skill set
In the gestation period of "The Sopranos," the all-important casting of the lead (Tony) evidently offered up to showrunner David Chase a number of actors who were considered but didn't get the role(or turned it down.)
Ray Liotta(turned it down)
Anthony LaPaglia
The guy who plays Silvio
The guy who plays Jackie Aprile, Sr.
Evidently, the guy who plays Jackie Aprile, Sr. came closest to getting the role...which is why we see the actor playing Jackie: he's Don material, a leader.
But the role went to James Gandolfini, and what's clear about that great casting -- in addition to Gandolfini's great presence and warmth as an actor -- is that he was a BIG GUY.
All the other guys considered to play Tony were normal sized, or short, or thin...but Gandolfini could sell Tony as "smart enough to run the organization, big and tough enough to beat up all challengers."
We hadn't really had size as an element of "the boss" in gangster pictures. Cagney and Bogart were dimuitive, as were Pacino and Pesci. DeNiro and Caan could sell physical toughness and threat...but they weren't big men.
And of course, creeping into the storyline year after year on The Sopranos was the fact that Tony's bigness slowly turned into fatness. As someone wrote, "Tony is a man of big appetites": for money, for sex, for food. He just keeps getting bigger, but never loses his edge.
I liked, early in the series, a flashback to when Tony was just the main henchman to Jackie Aprile, Sr. A short boss and his oversized sidekick. You can figure that Jackie was the brains, and Tony was the brawn -- a Furio of sorts. And when Jackie died, the brawn was ready to become the brains(by brainily putting Uncle Junior out there as a front man...)
PS. Perhaps to make sure that Gandolfini wasn't the fattest guy on the show, they soon brought in Bobby and the gay Mafioso to distract attention...