Beleaguer is only slightly more beautiful than besiege but has lost its original meaning of besieging towns and cities. Today it means to overburden with troubles. To beleaguer is to mentally beset from all sides persistently, as with work or worries.
The sound of this word is beautiful because it contains both liquid consonants, L and R, and all the other consonants are vocal, pronouced while vibrating the vocal cords. The past participle of this word is the most prevalent form of the word, as to be beleaguered by demands on our lives. However, someone who beleaguers others is a beleaguerer and the occupation of beleaguerers is beleaguerment (the action noun).
We no longer waste the beauty of this word on military sieges but save it for more personal sieges of worries and cares: “When beleaguered by the cares of office, Franklin enjoyed retiring to the subdued inner sanctum of his study alone with a Grisham novel.” People beleaguer us only so long as they are persistently bothersome: “Constantly beleaguered by reporters bellowing trivial questions, Lucille was beginning to regret the fame she had worked so hard to achieve.”
English borrowed this one from a related Germanic language, Dutch. The Dutch word belegeren is made up of be- “around” + leger “camp” + a verbal ending. The Proto-Indo-European root ambi “around, both (sides),” as in ambidextrous and amphibian, was reduced in the Germanic languages to be- in English and Dutch and um “around, about” in German. The root of leger comes from the same source as English lair (the root of which is lay). In German lager is the word for “camp,” as in that ugliest of words, Konzlager “concentration camp.” But it also means “layer, deposit,” so that the beer produced by six months storage to allow a layer of sedimentation to form is also called “lager beer.”