Gutter
Middle English: from Old French gotiere, from Latin gutta ‘a drop’; the verb dates from late Middle English, originally meaning ‘cut grooves in’ and later (early 18th century) used of a candle which melts rapidly because it has become channelled on one side.
wiktionary
From Middle English gutter, guttur, goter, from Anglo-Norman guttere, from Old French goutiere (French gouttière), ultimately from Latin gutta(“drop”).
gut + -er
etymonline
gutter (n.)
late 13c., "watercourse, water drainage channel along the side of a street," from Anglo-French gotere, Old French guitere, goutiere "gutter, spout" of water (12c., Modern French gouttière), from goute "a drop," from Latin gutta "a drop" (see gout). Meaning "furrow made by running water" is from 1580s. Meaning "trough under the eaves of a roof to carry off rainwater" is from mid-14c. Figurative sense of "low, profane" is from 1818. In printers' slang, from 1841.
gutter (v.)
late 14c., "to make or run in channels" (transitive), from gutter (n.). Intransitive use, in reference to candles (1706) it is from the channel that forms as the molten wax flows off. Related: Guttered; guttering.