Mr. Wilson is described as fat and red-faced, so he probably is not very active or inquisitive.
Watson describes Mr. Wilson this way as being overweight and red in the face.
I HAD CALLED upon my friend, Mr. Sherlock Holmes, one day in the autumn of last year and found him in deep conversation with a very stout, florid-faced elderly gentleman with fiery red hair.
The man’s physical characteristics might explain what made him a good mark in the first place. He does not seem to have spent a lot of time in his basement. It allowed his “assistant” to tunnel into the bank next door without drawing his attention.
Of course, the red hair gave them an excuse to create the “Red-Headed League.” It is a unique characteristic. Without that red hair, what else would they have been able to call upon? It does not specifically identify a personality trait, but it makes him stand out.
Our visitor bore every mark of being an average commonplace British tradesman, obese, pompous, and slow. ... Altogether, look as I would, there was nothing remarkable about the man save his blazing red head ...
Watson does not seem overly impressed by the man. His main traits seem to be his pride, his hair, and the fact that he is fat. All of this make him easy pickings for the criminals.
Characterization comes in two forms- physical traits and personality traits. Sometimes a character's outward appearance can be as useful to an author as his inward traits. In this case, making Wilson fat helped make him slow, and stereotypically stupid.