From PIE *kewk- (to curve, to arch) — the original concept of height was not linear but the curving vault of an arch or hill.
Of great vertical extent; extending far upward; far above ground or sea level; great in amount, value, size, or intensity.
From Old English 'hēah' (also 'hēh'), from Proto-Germanic *hauhaz, from PIE *kewk- meaning 'to curve, to arch, to vault.' The original image was of something arched or vaulted — height conceived as an upward curving. The same PIE root may have produced Lithuanian 'kaũkas' (bump, lump) and possibly Latin 'cumulus' (heap, mass), though these connections are
The PIE root behind 'high' (*kewk-) originally meant 'to curve or arch,' not 'tall' — height was first conceived as an upward vaulting, like the curve of a hill or an arched ceiling. The spelling of 'high' with 'gh' preserves a guttural consonant (like German 'ch' in 'hoch') that was still pronounced in Middle English but fell silent by the 1500s.