hat (n.)youdaoicibaDictYouDict[hat 词源字典]
Old English hæt "hat, head covering" (variously glossing Latin pileus, galerus, mitra, tiara), from Proto-Germanic *hattuz "hood, cowl" (cognates: Frisian hat, Old Norse hattr, höttr "a hood or cowl"), from PIE root *kadh- "cover, protect" (cognates: Lithuanian kudas "tuft or crest of a bird," Latin cassis "helmet"). To throw one's hat in the ring was originally (1847) to take up a challenge in prize-fighting. To eat one's hat (1770), expressing what one will do if something he considers a sure thing turns out not to be, is said to have been originally eat Old Rowley's [Charles II's] hat.[hat etymology, hat origin, 英语词源]
sure (adj.)youdaoicibaDictYouDict
early 13c., "safe against attack, secure," later "firm, reliable" (c. 1300); "mentally certain, confident" (mid-14c.); "firm, strong, resolute" (c. 1400), from Old French seur, sur "safe, secure; undoubted, dependable, trustworthy" (12c.), from Latin securus "free from care, untroubled, heedless, safe" (see secure (adj.)). Pronunciation development is that of sugar (n.).

As an affirmative meaning "yes, certainly" it dates from 1803, from Middle English meanings "firmly established; having no doubt," and phrases like to be sure (1650s), sure enough (1540s), and for sure (1580s). The use as an adverb meaning "assuredly" goes back to early 14c. Sure-footed is from 1630s, literal and figurative; sure thing dates from 1836. In 16c.-17c., Suresby was an appellation for a person to be depended upon.