grade (n.)
1510s, "degree of measurement," from French grade "grade, degree" (16c.), from Latin gradus "step, pace, gait, walk;" figuratively "a step, stage, degree," related to gradi "to walk, step, go," from PIE *ghredh- (cognates: Lithuanian gridiju "to go, wander," Old Church Slavonic gredo "to come," Old Irish in-greinn "he pursues," and second element in congress, progress, etc.).

Replaced Middle English gree "step, degree in a series," from Old French grei "step," from Latin gradus. Railway sense is from 1811. Meaning "class of things having the same quality or value" is from 1807; meaning "division of a school curriculum equivalent to one year" is from 1835; that of "letter-mark indicating assessment of a student's work" is from 1886 (earlier used of numerical grades). Grade A "top quality, fit for human consumption" (originally of milk) is from a U.S. system instituted in 1912.
grade (v.)
1650s, "to arrange in grades," from grade (n.). Related: Graded; grading.