Columbia Pictures is keeping Worcester guy Denis Leary busy with the promotion of “The Amazing Spider-Man,” which comes out July 3. On Monday the actor/comedian was in New York with his director Mark Webb and costars Emma Stone, Rhys Ifans, and Andrew Garfield lighting up the Empire State Building in honor of the organization Stand Up to Cancer. Leary is Captain Stacy in “Spider-Man,” a role that was played by James Cromwell, back when Tobey Maguire was the web-shooting superhero.