The speaker in "The Weary Blues" never reveals to us who he actually is. However, we know that he is involved to an extent in the jazz scene on Lenox Avenue; he knows not only the meaning of technical musical features as syncopation, but also what happens to the "Negro" piano player at the end of the night.
We can assume that the speaker has an affinity with the blues, based on his exhortations--"O Blues!" He also seems to have a particular interest in music, which might echo from "a black man's soul."
The final stanza of this poem is what really complicates the matter. The speaker, it seems, is not a simple bystander. If this were the case, how could he know that the pianist "slept like a rock or a man that's dead" after his concert? We could interpret this stanza as a step outside the scene of the poem as the speaker becomes somewhat omniscient. Alternatively, we could infer that the narrator knows the piano player or that the narrator is sufficiently familiar with the scene, and with the feelings of people in the black community, to begin to imagine how the man might have slept after such a performance.
The ultimate answer to this question is that we do not know, but we do know that the speaker is someone who is interested in communicating to the wider world what this community values.