I learned the story behind the song from the liner notes on a Breslover album I picked up a while back. The album is titled "Nigunei Neshama" and is a live recording of "beautiful old melodies that arouse one to the service of Hashem, which were sung from time to time in the house of Reb Levi Yitzchak Bender z"l, the head of chasidei Breslov in Eretz Yisrael."
The tune was composed by Reb Meir Leib Blekher z”l. Being extremely poor, and not having anything to give his daughter on her wedding day, he went out to meditate and pray in the fields. When he returned, he said to her: “A wedding dress I don’t have for you, however a nice melody I do have [for you]!” He then began to sing this song to the verse from Eshet Chayil – Oz VeHadar... [as if to say] the main thing is the garment for the Last Day. (Siach Sarfei Kodesh, 3-398)A lot of people think this is a Carlebach tune. I blame Soulfarm!