Lyric discussion by vtwo 

Cover art for Quarter Past lyrics by Fall of Troy, The

It could be about a girl. It could be about a drug. It could be about a girl becoming like a drug.

If the girl becomes like a drug, according to the lyrics, "I" throws "her" out the window which leads me to think that the song is purely about drugs.

If it's about drugs, he goes to his window to smoke (I'm assuming - "sing you to sleep").

Word to ya mutha!