'light-tailed' is formed in Modern English from the adjective 'light' and the noun 'tail'. 'light' originates from Old English, specifically the word 'līht' (or variants) where it meant 'not heavy'; 'tail' originates from Old English, specifically the word 'tægl'/'tægel', where it meant 'an appendage or projecting part'.

'light' (Old English 'līht') and 'tail' (Old English 'tægl') combined in English to form compounds such as 'light-tailed' with the adjectival '-ed' formation; the literal compound ('having a light tail') existed earlier, and the figurative/statistical sense ('having rapidly decaying tails') developed later, notably in 20th-century probability/statistics literature.

Initially it referred to a physically light or small tail; over time it gained a specialized figurative meaning in statistics to describe distributions whose tails decrease rapidly (the current common technical sense).