Though this doesn’t appear in my door-stopper OED, it seems to refer to eel-catching using a squirmy-wormy glob of bait, the person doing the babbing being a babber. ‘She saw him lift his rod and bring two eels at once hanging from a big reddish lump at the end of his line … “Babbing,” said Tom … As he spoke up came another eel biting hard in to the lump of worms, and letting go when he found himself in the air only to drop into the eel-babber’s big bucket.’ Source: Arthur Ransome, Coot Club (London: Jonathan Cape, 2009 (1934)), p. 276
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