軽視＝underestimate/take something lightly/not much think of 軽蔑＝despise someone/look someone scornful/dishonor 軽蔑 only can be used for persons or person's activity.軽視 can be used not only for persons, but for the influence or an accident. 軽蔑 meaning contains the feeling that subjective person look down on the objective person.