What role does the speaker assign to the "dear friend" in line 13, in relation to the metaphors of the poem?

The speaker begins by noting how he remembers good things from the past. But then he recalls things he did not accomplish or achieve. And he feels that in wailing about these "old woes," he is wasting his (present) time. He cries and this is illustrated by the metaphor to "drown an eye." He is overcome with nostalgia for people he had known who have died in the past. His now present weeping is about things he has wept about in the past. It is as if he is reliving his past "woe." He uses the metaphor of paying an old debt again to symbolize how he is reliving this misery: 

And heavily from woe to woe tell o'er 

The sad account of fore-bemoaned moan, 

Which I new pay as if not paid before. 

The mourning he is going through seems new, as if he never went through it in the past. The solution or cure to his misery of reliving his past regrets and sorrows is to focus on the present. Therefore, his "dear friend" is someone who is alive and well in the present. His dear friend functions as a hero or the cure to his obsession with the past.