Robb, I would have thought the "Baby Don't You Weep" releases by Fred Bridges and Edward Hamilton owe their genesis to the traditional gospel standard "Mary Don't You Weep". There have been a multitude of songs over the years with the title "Baby/Mary Don't you Weep " , certainly well before the Fred Bridges and Edward Hamilton records, done as slow ballads as well as rousing uptempo and often with the title and lyrics altered in any number of ways. It's a bit clever really of Fred Bridges and Harrison Smith to claim authorship of the song but to be fair to them they weren't the first to claim authorship of such standard gospel tunes. Very much like the numerous versions of that other standard "Wade In The Water". Admittedly Edward Hamilton's record uses the title "Baby Don't You Weep" but the lyrics bear little resemblance to the gospel standard.
Anyway here's a short history of the gospel tune Mary Don't You Weep:
The song tells the Biblical story of Mary of Bethany and her distraught pleas to Jesus to raise her brother Lazarus from the dead. Other narratives relate to The Exodus and the Passage of the Red Sea, with the chorus proclaiming Pharaoh's army got drown-ded!, and to God's rainbow covenant to Noah after the Great Flood. With liberation thus one of its themes, the song again become popular during the 1950's and 1960's American Civil Rights Movement. Additionally, a song that explicitly chronicles the victories of the Civil Rights Movement, "If You Miss Me from the Back of the Bus", written by Charles Neblett of The Freedom Singers, was sung to this tune and became one of the most well-known songs of that movement. The first recording of the song was by the Fisk Jubilee Singers in 1915. The best known recordings were made by the vocal gospel group The Caravans in 1958, with Inez Andrews as the lead singer, and The Swan Silvertones in 1959. "Mary Don't You Weep" became The Swan Silvertones' greatest hit, and lead singer Claude Jeter's interpolation "I'll be a bridge over deep water if you trust in my name" served as Paul Simon's inspiration to write his 1970 song "Bridge over Troubled Water". The spiritual's lyric God gave Noah the rainbow sign, no more water the fire next time inspired the title for The Fire Next Time, James Baldwin's 1963 account of race relations in America. Many other recordings have been made, by artists ranging from The Soul Stirrers to Burl Ives. Pete Seeger gave it additional folk music visibility by performing it at the 1964 Newport Folk Festival, and played it many times throughout his career, adapting the lyrics and stating the song's relevance as an American song, not just a spiritual. In 1960, Stonewall Jackson recorded a country version of the song, where Mary is a young woman left by her lover on the wedding day to fight in the civil war, and he died in the burning of Atlanta; the song became a hit when it peaked at #12 in Country charts and #41 in Pop charts. In the 1960's, Jamaican artist Justin Hinds had a ska hit with "Jump Out Of The Frying Pan", whose lyrics borrowed heavily from the spiritual. Paul Clayton's version "Pharaoh's Army" appears in "Home-Made Songs & Ballads", which was released in 1961. James Brown rewrote the lyrics of the original spiritual for his 1964 soul hit "Oh Baby Don't You Weep". Aretha Franklin recorded a live version of the song for her 1972 album Amazing Grace. An a cappella version by Take 6, simply called "Mary", received wide airplay after appearing on the group's eponymous debut album in 1988. The song is sung briefly at the beginning of the music video for Bone Thugs N Harmony's 1996 "Tha Crossroads".