Lexicographic ordering is non-zero weight. (Well, sort of. You can't represent a lexicographic ordering with a real-valued social welfare function, so nothing will have "weight" in that sense, but you get the point.)

Lexicographic ordering is zero weight outside of toy problems, since even the smallest possibility of making a difference at the highest order will exclude even the greatest possibility of making a difference at lower orders from attention – but this may have been the point of your previous comment.