Entries linking to nestling
"structure built by a bird or domestic fowl for the insulation and rearing of its young," Old English nest "bird's nest; snug retreat," also "young bird, brood," from Proto-Germanic *nistaz (source also of Middle Low German, Middle Dutch nest, German Nest; not found in Scandinavian or Gothic), from PIE *nizdo- (source also of Sanskrit nidah "resting place, nest," Latin nidus "nest," Old Church Slavonic gnezdo, Old Irish net, Welsh nyth, Breton nez "nest"), probably from *ni "down" + from PIE root *sed- (1) "to sit."
From c. 1200 of an animal or insect. Used since Middle English in reference to various accumulations of things, especially of diminishing sizes, each fitting within the next (such as a nest of drawers, early 18c.). Nest egg "retirement savings" is from 1700; it was originally "a real or artificial egg left in a nest to induce the hen to go on laying there" (nest ei, early 14c.), hence "something laid up as the beginning of a continued growth."
Both these suffixes had occasional diminutive force, but this was only slightly evident in Old English -ling and its equivalents in Germanic languages except Norse, where it commonly was used as a diminutive suffix, especially in words designating the young of animals (such as gæslingr "gosling"). Thus it is possible that the diminutive use that developed in Middle English is from Old Norse.