In prior posts, I've been babbling about all these meanings applied to *mar-, *mer- or *smer- by Indo-Europeanists and how skeptical I am of one particular set of meanings in this clumsy word pile, that revolving around the notions of 'shimmer' and 'shine'. I recently found an instructive account of this whole messy group of words, published in French: Skoda, Le redoublement expressif: Un universal linguistique. Analyse du procédé en grec ancien et en d'autres langues (1982), pp.120-2.
I strongly suspect that there lies an Aegean root underneath this and it has nothing to do with Proto-Indo-European at all. However with what little we know of the Aegean group (ie. Etruscan, Lemnian, Minoan, etc.) and with some even denying that such a group exists, etymologists don't seem to be getting very far here. Half-solutions everywhere; nothing tied together very well.
Let's cut to the chase and propose something bold and new. Let's say for a moment that there's a Proto-Aegean verb *amára 'to reflect, to shine'. Let's say that it remained unchanged in later Minoan. Let's also say that this same root however was reduced to Proto-Cyprian *mar from which we should expect the same in Etruscan, Eteo-Cretan, etc. Let's then run with this and say that there's a derivative *amária meaning 'reflection, shine' which is again preserved in Minoan while reduced to *mera in Proto-Cyprian. From 'reflection' come the notions of 'appearance' and 'face' in a similar fashion to that of Japanese 色 (iro) 'colour; appearance'.
What's the point of all my crazy theorizin'? Have I cracked? Probably, but damned if this doesn't give an interesting alternative solution to a plethora of poorly etymologized or unetymologized words in Greek using a fresh non-IE perspective:
- ἀμαρυγή (amarugḗ) 'a sparkle'
- ἀμάρυγμα (amárugma) 'a sparkle'
- ἀμαρύσσω (amarússō) 'to sparkle, to glance'
- μαραυγέω (maraugéō) 'to contract the pupil in light'
- μαραυγία (maraugía) 'dazzling of the eyes'
- μαρμαίρω (marmáirō) 'to sparkle, flash, glitter'
- μαρμάρεος (marmáreos) 'flashing, glittering'
- μάρμαρος (mármaros) 'sparkling stone; marble'
 Consult for example Beekes' Greek Etymological Dictionary under ἀμαρύσσω.