Great song by Bon Iver, about a relationship, not about a skinny woman but a relationship that the lead singer kept going because he needed help but he recognised the relationship was skinny in the sense that it didn't have weight and was going to fail. Justin Vernon the lead of Bon Iver stated that "skinny love doesn't have a chance because it is not nourished"
Read more here about the song
https://genius.com/Bon-iver-skinny-love-lyrics
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