brimful (adj.)

"brink, edge, margin," c. 1200, brymme "edge (of the sea), bank (of a river)," a word of obscure origin, chiefly Northern, which is probably from or related to dialectal German bräme "margin, border, fringe," from PIE *bhrem- "point, spike, edge." It was extended by 1520s to the upper or projecting edge of anything hollow (cups, basins, hats).

Old English (and northern Middle English) had brim "sea, surf, pool, spring, river, body of water," of uncertain origin perhaps akin to Old Norse barmr "rim, brim." "It became obs. in ME.; but was perhaps used by Spenser" [OED].

word-forming element attached to nouns (and in modern English to verb stems) and meaning "full of, having, characterized by," also "amount or volume contained" (handful, bellyful); from Old English -full, -ful, which is full (adj.) become a suffix by being coalesced with a preceding noun, but originally a separate word. Cognate with German -voll, Old Norse -fullr, Danish -fuld. Most English -ful adjectives at one time or another had both passive ("full of x") and active ("causing x; full of occasion for x") senses.

It is rare in Old English and Middle English, where full was much more commonly attached at the head of a word (for example Old English fulbrecan "to violate," fulslean "to kill outright," fulripod "mature;" Middle English had ful-comen "attain (a state), realize (a truth)," ful-lasting "durability," ful-thriven "complete, perfect," etc.).