A reason why so many bluesmen were blind can be found in the circumstance is in a word, malnutrition. In the areas that blues was born, the Mississippi Delta and West Texas, black people were almost universally share croppers. This is because a huge proportion of black property, wealth and opportunity was taken from them during the ‘Jim Crow’ era.
As a share cropper, blacks lived off of a very small portion of the food they grew, giving the rest to their landlord as rent. Living almost entirely off of cereals and corn, they often didn't get enough vitamin A as children and therefore went blind. As you might imagine, being a blind, black 12 year old in the deep South during the Nadir of Race Relations meant you had virtually no avenues to simply stay alive. Preaching, gospel singing and then the blues were just about the only way to survive the situation. (James J. Kelly III)
Malnutrition is certainly a cause of blindness, but as the descriptions below show, there are several causes. The career of musician was one of the few open to those born blind in the Deep South. Many of them developed a heightened musicality and interest in music.

Theodore Roosevelt "Blind Teddy Darby"
Teddy lost his eyesight because of glaucoma (he was 20 years old when it happened, glaucoma is a disease of the optic nerve, which if left untreated can lead to blindness). In the late 1930s, he gave up the blues and became an ordained deacon (a layperson who, after ordination, is authorized to perform various religious rituals and ceremonies). His stage name comes from “Teddy” Theodore Roosevelt (President of the United States from 1901 to 1908).

Le Moise "Blind" Roosevelt Graves
He played with his brother Uaroy Graves, who was also nearly blind and played the tambourine. They were credited as "Blind Roosevelt Graves and Brother". The name of his brother "Uaroy" was so unusual that it was also written as "Leroy" or "Aaron".

Saunders "Sonny Terry" Terrell
He sustained injuries to his eyes and went blind by the time he was 16, which prevented him from doing farm work, and was forced to play music in order to earn a living, Terry established a long-standing musical relationship with Walter Brown "Brownie" McGhee. His stage name is a phonetic spelling of his first and surname.

Note
“Blues In My Soul” (Prestige Records, Sonny Terry and Brownie McGhee, 1960) was the first LP to introduce me to blues music.

Gary D. Davis a.k.a. "Blind Gary Davis" and "Reverend Gary Davis"
He became blind as an infant. He'd recall his grandmother telling him he got "sore eyes" when he was three-weeks old, and the doctors put something in his eyes that "cause ulcers to grow" over the eyes and he ended up blind. In 1933 he was ordained and became a minister of the Baptist Church, performing only in spiritual songs, earning the stage name "Reverend Gary Davis."

William Samuel "Blind Willie McTell" McTier
McTell (phonetic spelling of McTier) was born blind in one eye and lost his remaining vision by late childhood. He attended schools for the blind in Georgia, New York and Michigan and showed proficiency in music from an early age, first playing the harmonica and accordion, learning to read and write music in Braille. in the 1920s, he left his hometown and became an itinerant musician, or "songster" (a wandering musician).

Arthur "Blind" Blake
He was born blind. Nothing else is known of Blake until the 1920s, when he emerged as a recording musician.
Big Bill Broonzy, hearing Blake in person in the early 1920s, said of his guitar playing "He made it sound like every instrument in the band- saxophone, trombone, clarinets, bass fiddles, pianos- everything. I never had seed then and I haven't to this day yet seed no one that could take his natural fingers and pick as much guitar as Blind Blake.

Blind Joe Reynolds
He was blinded by a shotgun blast to the face in Louisiana in the mid-late 1920s. Despite this handicap, Blind Joe became known for his distinctive bottleneck style as well as his reported accuracy with a pistol.
Eric Clapton borrowed the slide lick for the first Cream album.

Lemon Henry "Blind Lemon" Jefferson
He was one of the most popular blues and gospel singers of the 1920s. Lemon was born blind. He died in 1929 at the age of 36 from myocarditis; an inflammation of the heart muscle, which is usually caused by a virus.
His recordings for Paramount brought him success and enough money to purchase a car and hire a driver. Jefferson is known for traveling unusually extensively in the southern United States for that time.
Jefferson had an intricate and fast style of guitar playing and a particularly high-pitched voice. He was a founder of the Texas blues sound and an important influence on other blues singers and guitarists, including Lead Belly and Lightnin' Hopkins. His songs "Matchbox Blues" was recorded more than 30 years later by the Beatles, in a rockabilly version.

John Adam "Sleepy John" Estes
John had an eye disease that caused him to have hooded eyes, which gave him the nickname Sleepy, and later in life he became blind.
Estes himself explained that the nickname was born of his exhausting life as both musician and farmer. "'Every night I was going somewhere. I'd work all day, play all night and get back home about sunrise. I'd get the mule and get right on going. I went to sleep once in the shed. I used to go to sleep so much when we were playing, they called me Sleepy. But I never missed a note.'"
His wife Ann took many of the iconic photos of Estes found in blues books and album covers.

Charles Pertum, known professionally as Charlie "Specks" McFadden
McFadden used Charles "Speck" Pertum as his name on a couple of his earliest recordings, and also used the nickname "Black Patch", both nicknames referring to his reported "weak eyes". On most of his recordings he used his stepfather's name, McFadden.
McFadden's most notable number was "Groceries on the Shelf (Piggly Wiggly)". "Piggly Wiggly" is the name of a supermarket chain operating in the Southern and Midwestern regions of the United States.