Bleachers were used in a pinch as uncovered overflow seating from the grandstand before they became common at baseball and football games.
The first recorded printed reference was in the Chicago Tribune on May 6, 1889.
They were called “bleachers” because of their exposure to the sun.
The folding seating at an inside gymnasium simply took its name from the open seating outside.
That’s why the extra seats in a gymnasium or open-air benches in a stadium are called “bleachers”.