Old English heanes; see high (adj.) + -ness. Meaning "royalty, excellence, nobility" is early 13c.; Your Highness as a form of address to English royalty is attested from c. 1400.
responsible for the highness of the rates
Highlander
highlight
highlighter
highly
high-minded
highness
high-pitched
high-powered
high-pressure
high-rise
high-roller