Most syncopated tunes aren't considered drowsy, because syncopation makes the rhythm bounce in a lively way. Honky-tonk music is the exception and was played in bars with bad reputations; like the one in the poem. Such a "low" form of music is an interesting contrast to the "high art" of lyric poetry.
He did a lazy sway…. He did a lazy sway…. (6-7)
In the poem, Hughes employs some typical blues forms. The repetition keeps the song simple, but lets the performer improvise some fancy guitar or piano riffs the second time around.
With his ebony hands on each ivory key He made that poor piano moan with melody. (9-10)
Being creative is hard work. The act of putting your body and soul into making the best song can be a painful process. Here the singer is putting his own frustrations into the music, and his instrument seems to telegraph the pain to the audience.
He played that sad raggy tune like a musical fool.
Ragtime had been around for about twenty years when Hughes wrote this poem, and it was pretty popular across cultures. Scott Joplin, known for originating ragtime, was a classically trained musician, but ragtime was popular with many people. By making the music raggy, the speaker is connecting the music to the common people that Hughes was so fond of.
"I's gwine to quit my frownin'" (21)
In this line, the grammar isn't standard and the spelling mimics a very strong accent. This puts some cultural distance between the singer and the speaker, who uses Standard English. However, the dialect lyrics could be for show, because the musician thinks that they make the music sound authentic. He is giving a performance. You don't talk to your grandma the same way you talk to your friends, do you?
While the Weary Blues echoed through his head. (34)
The musician has the song stuck in his head. It was such a catchy melody that he can't get it out.