Mary --

Actually, here I'm using "weep" in a semi-metaphorical way, as a symbol of being simply overwhelmed by circumstance.

I don't sing these songs to keep the tears from falling, exactly, but to give me the strength to pick myself up after I soak my pillow and get back out there.

But you're right. In this culture, especially, we often feel the need to be given permission to cry, and sad, weepy songs do that. They give us the sense that we're not the only ones who've felt this way -- the composer of the song did, too.