league

In the sense of an alliance, league comes from Middle English liege/ligue, from Middle French ligue, from Italian lega, from the verb legare, ultimately from Latin ligō, "to tie." In the sense of a unit of distance, league comes from Middle English lege, from Late Latin leuca/leuga, "the Gaulish mile," from Gaulish, from Proto-Celtic *lougā.

These two meanings never merged from a single root — they simply arrived in English as separate words that happened to end up spelled and pronounced alike: one rooted in the idea of tying people together, the other in an old Gaulish measure of walking distance.

The distance sense of league is a doublet of legua, the Spanish and Portuguese unit of distance, since both descend from the same Late Latin leuca.