Unduly means more than is normal, fair, or reasonable — 'too much, and that is a problem'. It is an adverb, so it attaches to adjectives and verbs: 'unduly worried', 'unduly harsh', 'unduly optimistic', 'don't worry unduly'. Why not just say 'too'? Because 'too' is blunt and 'unduly' is measured. 'Too worried' sounds like ordinary talk. 'Unduly worried' sounds like someone weighing the situation and delivering a judgement: given the facts, your worry has gone past what the facts support. So it belongs to careful, considered English — doctors, lawyers, teachers, official letters, serious journalism. Two friends do not say 'you're unduly anxious'; they say 'you're stressing too much'. Look at where it actually appears, because this is the part students find useful. The single most common home for it is the negative, softly reassuring sentence: 'I wouldn't worry unduly.' 'She was not unduly concerned.' 'This need not unduly alarm us.' Here the speaker is calming someone down without pretending there is nothing at all to worry about — they are saying the worry exists, but it should not be big. That is a very English kind of gentleness, and 'unduly' is one of its favourite tools. It sits with words about feeling and judgement: worried, concerned, alarmed, harsh, generous, influenced, pessimistic, difficult, long. Though actually — 'unduly generous' is worth a second look, since generous is a good thing. The word can still attach, because it is not judging good vs bad; it is judging appropriate vs excessive. Even a good quality can go past the right amount.