"to feed," Old English grasian "to feed on grass," from græs "grass" (see grass). Cf. Middle Dutch, Middle High German grasen, Dutch grazen, German grasen. Figurative use by 1570s. Related: Grazed; grazing.
"to touch," c.1600, perhaps a transferred sense from graze (v.1) via a notion of cropping grass right down to the ground (cf. German grasen "to feed on grass," used in military sense in reference to cannonballs that rebound off the ground). Related: Grazed; grazing. As a noun from 1690s.
To eat small amounts often: ''I don't eat meals,'' she said. ''I graze all day long''/ Cindy Crawford grazing at the salad bar (1980s+)