"either of the dishes of a balance," 1830, from scale (n.2) + pan (n.).
Entries linking to scale-pan
scale n.2
[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.
pan n.
"broad, shallow vessel of metal used for domestic purposes," Middle English panne, from Old English panne, earlier ponne (Mercian) "pan," from Proto-Germanic *panno "pan" (source also of Old Norse panna, Old Frisian panne, Middle Dutch panne, Dutch pan, Old Low German panna, Old High German phanna, German pfanne), probably an early borrowing (4c. or 5c.) from Vulgar Latin *patna. This is supposed to be from Latin patina "shallow pan, dish, stew-pan," from Greek patane "plate, dish," from PIE *pet-ano-, from root *pete- "to spread."
But both the Latin and Germanic words might be from a substrate language [Boutkan]. Irish panna probably is from English, and Lithuanian panė is from German.
The word has been used of any hollow thing shaped somewhat like a pan; the sense of "head, top of the head" is by c. 1300. It was used of pan-shaped parts of mechanical apparatus from c. 1590; hence flash in the pan (see flash (n.1)), a figurative use from early firearms, where a pan held the priming (and the gunpowder might "flash," but no shot ensue). To go out of the (frying) pan into the fire "escape one evil only to fall into a worse" is in Spenser (1596).