To hold, brandish, or wield something with skill or power.
From Middle English 'be-' + 'wield' (to hold and use a weapon or tool). While 'wield' alone means to hold and use effectively, 'bewield' intensified or emphasized the action, though the distinction between the two forms is subtle and the prefix version fell out of use.
Most English speakers only know 'wield' today, but adding 'be-' to verbs was how Middle English speakers emphasized actions—kind of like how we might say 'really wielded' instead of just 'wielded.' The fact that 'bewield' didn't survive while 'wield' did shows that not all prefix experiments stick around.
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