Lyric discussion by chewyballer 

Cover art for Sleepless lyrics by Decemberists, The

I think the speaker is talking about death of a loved one, perhaps a family member, in a hospital room.

"As you lie before me now, like a shadow On a pea green sea Never thought that I could find you so hollow"

I agree that the ocean/water metaphor represents a kind of slow drowning, drowning in sorrow.
The speaker also mentions money. I think this is key to the story.

"A field of tears that will never yield a single penny

Wished for gold so I could buy you a palace By the riverside You'd come in and I would fill your diamond chalice You were still alive"

The speaker and his/her family could've been poor and unable to afford the treatment necessary to save the person who passed away.

"Did his eyelids fix on empty chairs You had traveled to lay beside? A gentle torture to watch it all recede And all the while your mother slept beside him"

In the above stanza, I can a scene where there are vacant chairs by the patient's hospital bed that he/she wished were filled with more friends, family or even the speaker himself other than his mother.

All this time, I think it's one person relating the story. But, then the voice changes into another character:

"Hand it over (hand it over) Hand it over (oh) You're weary, lay him down You did your time so thank you very much Hand it over (hand it over) Hand it over (oh) So now your hopes are all laid But you hand it all away"

Whoever is speaking here may be the cold subconscious truth edging out of his mind saying give up all hope (hand all hope over). But, I can also imagine them saying hand over all your money for the treatment and with it everything you own, including feelings of hope. "You did your time so thank you very much" is a very cold statement to make in light of death. This speaker gives no empathy and demands even more suffering upon the family.

Take my interpretation with a grain of salt please. I don't pretend to know what everything Colin means, but I think it really is a death of a loved one and how they can't afford to pay for the hospital bills (keeping with the theme of AIDS awareness).

Thanks, Chewy