Entries linking to betweenness
Old English betweonum, Mercian betwinum, "in the space which separates, midway, in the midst, among; by turns," from bi- "by" (see by) + tweonum dative plural of *tweon "two each" (compare Gothic tweih-nai "two each;" from PIE root *dwo- "two").
Between is literally applicable only to two objects; but it may be and commonly is used of more than two where they are spoken of distributively, or so that they can be thought of as divided into two parts or categories, or with reference to the action or being of each individually as compared with that of any other or all the others. When more than two objects are spoken of collectively or in divisibly, among is the proper word. [Century Dictionary]
In all senses, between has been from its earliest appearance, extended to more than two. [OED]
Between a rock and a hard place "caught in a dilemma, in a difficult situation" is from 1940s, originally cowboy slang (earlier was between the beetle (hammer) and the block, late 19c.). Between-whiles "at intervals" is from 1670s.
word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).