Old English faldan (Mercian), fealdan (West Saxon), transitive, "to bend (cloth) back over itself, wrap up, furl," class VII strong verb (past tense feold, past participle fealden), from Proto-Germanic *falthan, *faldan (source also of Middle Dutch vouden, Dutch vouwen, Old Norse falda, Middle Low German volden, Old High German faldan, German falten, Gothic falþan), from PIE *pol-to-, suffixed form of root *pel- (2) "to fold."
Of the arms, from late Old English. Intransitive sense "become doubled upon itself" is from c. 1300 (of the body); earlier "give way, fail" (mid-13c.). Sense of "to yield to pressure" is from late 14c. The weak conjugation developed from 15c. Related: Folded; folding.