Old English bolster "bolster, cushion, something stuffed so that it swells up," especially "a long, stuffed pillow," from Proto-Germanic *bolkhstraz (source also of Old Norse bolstr, Danish, Swedish, Dutch bolster, German polster), from PIE *bhelgh- "to swell," extended form of root *bhel- (2) "to blow, swell." Applied since 15c. to various parts which support others.
mid-15c. (implied in bolstered), "prop up; make to bulge" (originally of a woman's breasts), from bolster (n.). Figurative sense is from c. 1500, on the notion of "to support with a bolster, prop up." Related: Bolstering.