graze: [OE] There is no difficulty about the etymology of graze ‘feed on grass’: it was formed in Old English times as a derivative of the noun græs (modern English grass). But what about graze in the sense ‘scrape lightly’, first recorded in the 17th century? In the absence of any convincing alternative candidates, it is usually taken to be simply a special use of graze ‘feed on grass’, in the sense ‘remove grass close to the ground’, as some animals do in grazing – like a ‘close shave’, in fact. => grass
"to feed on grass," Old English grasian, from græs "grass" (see grass). Compare Middle Dutch, Middle High German grasen, Dutch grazen, German grasen. Transitive sense from 1560s. Figurative use by 1570s. Related: Grazed; grazing.
"to touch lightly in passing," c. 1600, perhaps a transferred sense from graze (v.1) via a notion of cropping grass right down to the ground (compare 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, "an act of grazing."