How is the missing dumbbell a important clue, and how did the whole case depend on it?

Holmes gathers the men in the shadows to watch the house. They see a figure in the study, moving about stealthily and leaning out the window, seemingly stirring the moat below him. The figure hauls something from the water, and at this moment Holmes signals; the group runs forward across the bridge and rings the bell. Ames lets them in, and Holmes rushes past him to see Cecil Barker standing in the study. Barker is aghast and angry, but Holmes points to a bundle hurriedly thrust under the table. He proclaims that this is what they were after.

Barker is stunned and wonders how Holmes knew about this. Holmes explains that he was looking for the missing dumbbell and deduced that, since there was water nearby, the dumbbell—probably used as a weight for something—would be there. He fished it out and looked at it, then put it back and sent the note saying the moat was to be drained.

He undoes the bundle and finds the dumbbell, boots, a knife, and clothing. Holding up the clothes he reads the label: 'Neal, Outfitter, Vermissa, U.S.A.' This was Vermissa Valley, a coal mining locale that Barker had told them in one of his earlier interviews was associated with Douglas’s first wife. This may also be the Valley of Fear.

Barker’s face goes through “anger, amazement, consternation, and indecision” (231). He says acridly that he will tell them nothing, to which the inspector says he will have to be kept in sight until they get a warrant.

How was the missing dumbbell an important clue and how did the whole case depend on it