c. 1300, smilen, "assume a facial expression or change of features indicative of amusement and pleasure," perhaps from Middle Low German *smilen (compare Middle High German smielen) or a Scandinavian source (such as Danish smile "smile," Swedish smila "smile, smirk, simper, fawn"), from Proto-Germanic *smil-, extended form of PIE root *smei- "to laugh, smile" (source also of Sanskrit smayate "smiles;" Latvian smiêt "to laugh;" Latin mirus "wonderful," mirari "to wonder;" Old English smerian "to laugh at, scorn," Old High German smieron "to smile"). Related: Smiled; smiling; smilingly.
It gradually pushed the usual Old English word, smearcian (modern smirk), into a specific, unpleasant sense. Of the eyes, from 1759. Figuratively (of Fortune, etc.), as indicating favor or encouragement, from c. 1400. In Middle English to smile still (c. 1400) was to smile to oneself.
The saying smile and the world smiles with you is by 1884, in quotation marks, in newspaper poetry. An early second line to it was, frown, and it frowns again. [1886, credited to E.L. Ellsworth, "Cleveland Leader"]
The Romance, Celtic, and Slavic languages tend to use a diminutive of the word for "laugh" to mean "smile" (such as Latin ridere "laugh;" subridere "smile"), perhaps literally "small laugh" or "low laugh."