borrowed from Greek, from álgos "pain" (perhaps from the same base as alégein "to show concern or regard [for]") + -ia-ia entry 1
Note:
In Lexikon der indogermanischen Verben (2. Auflage, 2001), H. Rix, referring to his own earlier publication, reconstructs for alégein an Indo-European verb *h2leg- "take care (of)," and links it with the base -legere in Latin dīligere "to hold dear, have regard for" (see diligent), intelligere "to discern, understand" (see intelligent), and neglegere "to disregard, fail to care for" (see neglect entry 1).