An Etymological Dictionary of Astronomy and Astrophysics

1. A degree or step in a scale, as of rank, advancement, quality, value, or intensity.
   

2. To arrange in a series of grades; class; sort (Dictionary.com).

Etymology (EN): From Fr. grade “grade, degree,” from L. gradus “step, pace, gait, walk;” figuratively “a step, stage, degree,” related to gradi “to walk, step, go,” and second element in congress, progress, etc.;
from PIE *ghredh-; cf. Lith. gridiju “to go, wander,” O.C.S. gredo “to come,” O.Ir. in-greinn “he pursues.”

Etymology (PE): Padâk, from Baluci padâk “step, stair, ladder” (ultimately from Proto-Ir. *padaka-), older form of Pers. pâyé “step, base,” from Mid.Pers. pâd, pây;
Av. pad-, cf. Skt. pat: Gk. pos, genitive podos; L. pes; PIE *pod-/*ped-.