browbeat v.

c. 1300, broue, plural broues, brouen, "arch of hair over the eye," also extended to the prominent ridge over the eye (early 14c.), from Old English bru (plural brua), which probably originally meant "eyebrow" (but also was used in the sense of "eyelash"), from Proto-Germanic *brus- "eyebrow" (source also of Old Norse brun), from PIE *bhru- "eyebrow" (source also of Sanskrit bhrus "eyebrow," Greek ophrys, Old Church Slavonic bruvi, Lithuanian bruvis "brow," Old Irish bru "edge"). The -n- in the Old Norse (brun) and German (braune) forms of the word are from a genitive plural inflection.

The sense was extended by c. 1200 to "the forehead," especially with reference to movements and expressions that showed emotion or attitude, hence "general expression of the face" (1590s). From c. 1400 as "the slope of a steep place."

Words for "eyelid," "eyelash," and "eyebrow" changed about maddeningly in Old and Middle English (and in all the West Germanic languages). The extension of Old English bru to "eyelash," and later "eyelid" presumably was by association of the hair of the eyebrow with the hair of the eyelid. The eyebrows then became Old English oferbrua "overbrows" (early Middle English uvere breyhes or briges aboue þe eiges). The general word for "eyebrow" in Middle English was brew, breowen (c. 1200), from Old English bræw (West Saxon), *brew (Anglian), from Proto-Germanic *bræwi- "blinker, twinkler" (source also of Old Frisian bre, Old Saxon brawa, Middle Dutch brauwe "eyelid," Old High German brawa "eyebrow," Old Norse bra "eyebrow," Gothic brahw "twinkle, blink," in phrase in brahwa augins "in the twinkling of an eye").

Old English beatan "inflict blows on, strike repeatedly, thrash" (class VII strong verb; past tense beot, past participle beaten), from Proto-Germanic *bautan (source also of Old Norse bauta, Old High German bozan "to beat"), from PIE root *bhau- "to strike."

Past tense form beat is from c. 1500, probably not from Old English but a shortening of Middle English beted. Of the heart, c. 1200, from notion of it striking against the breast.

The meaning "overcome in a contest" is from 1610s (hence the sense of "legally avoid, escape" in beat the charges, etc., attested from c. 1920 in underworld slang). The sense of "be too difficult for" intellectually or physically (by 1870) is behind the shrug-phrase beats me.

The meaning "strike cover to rouse or drive game" (c. 1400) is the source of beat around (or about) the bush (1570s), the metaphoric sense of which has shifted from "make preliminary motions" to "avoid, evade." The nautical sense of "make progress against the wind by means of alternate tacks" is from 1670s. Command beat it "go away" is recorded by 1906 (though "action of feet upon the ground" was a sense of Old English betan); it is attested in 1903 as newsboy slang for "travel without paying by riding on the outside of a train."