Old English spon "chip, sliver, shaving, splinter of wood," from Proto-Germanic *spe-nu- (source also of Old Norse spann, sponn "chip, splinter," Swedish spån "a wooden spoon," Old Frisian spon, Middle Dutch spaen, Dutch spaan, Old High German span, German Span "chip, splinter"), from PIE *spe- (2) "long, flat piece of wood" (source also of Greek spathe "spade," also possibly Greek sphen "wedge").
As the word for a type of eating utensil, c. 1300 in English (in Old English such a thing might be a metesticca), in this sense supposed to be from Old Norse sponn, which meant "spoon" as well as "chip, tile." The "eating utensil" sense is specific to Middle English and Scandinavian, though Middle Low German spon also meant "wooden spatula." To be born with a silver spoon in one's mouth is from at least 1719 (Goldsmith, 1765, has: "one man is born with a silver spoon in his mouth, and another with a wooden ladle").
Old English fedan "nourish, give food to, sustain, foster" (transitive), from Proto-Germanic *fodjan (source also of Old Saxon fodjan, Old Frisian feda, Dutch voeden, Old High German fuotan, Old Norse foeða, Gothic fodjan "to feed"), from PIE root *pa- "to feed." Intransitive sense "take food, eat" is from late 14c. Meaning "to supply to as food" is from 1818.