Peter Jones and Mr. Merryweather come into the story as it is nearing a climax. Jones is "the official police agent." He is from Scotland Yard. Mr. Merryweather is chairman of the bank directors. Watson describes him as:
...a long, thin, sad-faced man, with a very shiny hat and oppressively respectable frock-coat.
Holmes tells Watson:
I thought it as well to have Jones with us also. He is not a bad fellow, though an absolute imbecile in his profession. He has one positive virtue. He is as brave as a bulldog and as tenacious as a lobster if he gets his claws upon anyone.
These two men are minor characters. Mr. Jones will serve to make an official arrest of John Clay when he emerges from his tunnel into the bank's strongroom. This ends the story neatly, because Holmes and Watson do not have to become involved in arresting Clay and taking him off to jail. Jones not only does all that, but he informs Clay that he has three more men waiting to apprehend his partner right outside the front door of Jabez Wilson's pawnshop.
Mr. Merryweather is important to the story because he has to let the other three men into the bank's strongroom. Merryweather actually has to unlock a number of doors and gates. For the sake of creating a somber and ominous mood, Conan Doyle has Watson give a detailed description of their entry and of the interior of the strongroom once they get there.
...following the guidance of Mr. Merryweather, we passed down a narrow passage and through a side door, which he opened for us. Within there was a small corridor, which ended in a very massive iron gate. This also was opened, and led down a flight of winding stone steps, which terminated at another formidable gate. Mr. Merryweather stopped to light a lantern, and then conducted us down a dark, earth-smelling passage, and so, after opening a third door, into a huge vault or cellar, which was piled all round with crates and massive boxes.
Peter Jones has been wanting to get his hands on John Clay for years. He is very excited about this entrapment plan. This helps to communicate excitement to the reader. However, the author, Arthur Conan Doyle, makes sure to have his hero Sherlock Holmes foremost in apprehending Clay when the thief emerges from his tunnel. Holmes seizes the intruder by the collar and then knocks the pistol out of the man's hand with a blow from his hunting crop.