The verse repeated in a song, or the return of the theme at the end of each stanza; the chorus; refrain. Hence: That which is often repeated or which is dwelt upon; the main topic; as, the burden of a prayer.
In music, the burden is the drone or base in some musical instruments, and the pipe or part that plays it, such as a bagpipe or pedal point in an organ. Hence, the burden of song is that part repeated at the end of each stanza, i.e. the chorus or refrain.
To dream that you carry a heavy burden, signifies that you will be tied down by oppressive weights of care and injustice, caused from favoritism shown your enemies by those in power. But to struggle free from it, you will climb to the topmost heights of success.