A Dutch friend asked me about the etymology behind the English word eavesdropper, since the equivalent word in Dutch, luistervink, includes the word vink, finch. The verb to eavesdrop came after the noun eavesdropper, according to the OED. They both come much later than the noun eavesdrop, originally eavesdrip, for which the Dictionary has a citation dating from the year 868. The eavesdrip is defined as “The dripping of water from the eaves of a house; the space of ground which is liable to receive the rain-water thrown off by the eaves of a building”. This was important in Anglo-Saxon times, as there was “an ancient custom or law that prohibited a proprietor from building at a less distance than two feet from the boundary of his land, lest he should injure his neighbour's land by ‘eavesdrop’” (a direct quote from the OED).
The early 17th-century legal dictionary, Les Termes de la Ley: or, Certaine Difficult and Obscure Words and Termes of the Common Lawes and Statutes of This Realme, written by John Rastell and William Rastell (in both French and English – read here), describes eavesdroppers as those who stand under walls and windows by night or day to hear news, which they then carry to others to make strife and dispute among their neighbours. The entry goes on to say that eavesdroppers should be punishable in the courts. The offence of eavesdropping was abolished in the UK only in 1967 by the Criminal Law Act of that year (along with the offences of being a common scold or common night walker).
The word eaves, the overhanging edge of a roof, is from the same root as the word over. The s of eaves is due to the original Old English spelling of the word, efes, it was not originally a plural ending. However, eaves is treated as a plural noun these days because of the s at the end.