Surrounded or trapped by an enemy military force; or overwhelmed by constant demands or problems.
From 'besiege' (from 'be-' + 'siege'), where 'siege' comes from Old French 'siege' (seat/siege), derived from Latin 'sedere' (to sit). Armies would 'sit' around a city to starve it out.
The 'sed-' root meaning 'sit' is everywhere—sediment (stuff that settles), sedentary (staying seated), session (a sitting together)—and 'siege' captures the brilliant idea that conquering a city meant just sitting around it until people gave up, making patience a military weapon.
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