scale (n.1)

[one of the skin plates on fish or snakes] c. 1300, from Old French escale "cup, scale, shell pod, husk" (12c., Modern French écale), from Frankish *skala or some other Germanic source, from Proto-Germanic *skæla "to split, divide" (source also of Dutch schaal "a scale, husk," Old High German scala "shell," Gothic skalja "tile," Old English scealu "shell, husk"), from PIE root *skel- (1) "to cut." A prehistoric cognate of scale (n.2) "weighing instrument."

In reference to humans, as a condition of certain skin diseases, it is attested from late 14c. Extended in botany to coverings of leaf-buds, etc., by 1776. As what falls from one's eye when blindness ends (usually figurative), it echoes Acts ix:18 (Latin tanquam squamæ, Greek hosei lepides).

[weighing instrument] early 15c., extended to the whole instrument from the earlier sense of "pan of a balance" (late 14c.); earlier still "drinking cup" (c. 1200), from Old Norse skal "bowl, drinking cup," in plural, "weighing scale."

This is from a noun derivative of Proto-Germanic *skæla "to split, divide" (source also of Old Norse skel "shell," Old English scealu, Old Saxon skala "a bowl (to drink from)," Old High German scala, German Schale "a bowl, dish, cup," Middle Dutch scale, Dutch schaal "drinking cup, bowl, shell, scale of a balance"), from PIE root *skel- (1) "to cut."

The connecting sense seems to be of half of a bivalve ("split") shell used as a drinking cup or a pan for weighing; compare scallop, which is from the same root. But according to Paulus Diaconus the "drinking cup" sense originated from a supposed custom of making goblets from skulls (see skull). Scales as a name for the zodiac constellation Libra is attested in English from 1630s.

"to climb (a wall) by or as by a ladder; attack with scaling ladders," late 14c., scalen, from Latin scala "ladder, flight of stairs," from *scansla, from stem of scandere "to climb" (see scan (v.)).

Middle English scale, "ladder used in sieges," is attested c. 1400, from the Latin noun. The verb in general and figurative use (of mountains, heights of pleasure, etc.) is from 16c.

Via scale (n.3) "standard of measure or estimation" comes the meaning "measure or regulate by a scale" (1798), the sense of "draw, project, or make according to scale" (by 1885), and scale down "cut or decrease proportionally in every part" (by 1887). Related: Scaled; scaling.

"remove the scales of (a fish, etc.)," c. 1400, scalen, from scale (n.1). Intransitive sense "to separate and come off in scales or thin layers" is from 1520s. Related: Scaled; scaling.

1690s, "weigh in scales," from scale (n.2). Earlier in a now-obsolete sense "to compare, estimate" (c. 1600). The meaning "weigh out in proper quantities" is by 1841. Related: Scaled; scaling.

[standard of measure or estimation] late 14c., "series of registering marks; marks laid down to determine distance along a line," (in Chaucer's description of the astrolabe), from Latin scala "ladder, flight of stairs," from *scansla, from stem of scandere "to climb" (see scan (v.)). 

The noun in the classical Latin sense is rare, though Middle English had it as "ladder used in sieges" (c. 1400). The meaning "succession or series of steps ascending or descending" is from c. 1600; that of "standard for estimation" (large scale, small scale, etc.) is from 1620s.

The musical sense of "definite and standard series of tones within a certain range," typically an octave (1590s), and the meaning "proportion of a representation to the actual object" (1660s) are via Italian scala, from Latin scala.