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Old English alecgan "to put down, remit, give up," a Germanic compound (cf. Gothic uslagjan, Old High German irleccan, German erlegen), from a- "down, aside" + lecgan "to lay" (see lay).
Early Middle English pronunciations of -y- and -g- were not always distinct, and the word was confused in Middle English with various senses of Romanic-derived alloy and allege, especially the latter in an obsolete sense of "to lighten," from Latin ad- "to" + levis (see lever).
Amid the overlapping of meanings that thus arose, there was developed a perplexing network of uses of allay and allege, that belong entirely to no one of the original vbs., but combine the senses of two or more of them. [OED]The double -l- is 17c., a mistaken Latinism. Related: Allayed; allaying.