Green’s Dictionary of Slang

to snatch, to grab, to seize; thus grabble the bit v., to snatch someone’s money.

c.1700		ballad in J. Adland Restoration Bawdy 98: Nelly, though he teized her, / And grabbled her and squeezed her / Cried, ‘Stay a little’.
1781		G. Parker View of Society II 62: The Kiddy Nipper, who has a pair of scissors about him, sits on the side of the man whom he has destined for his prey [...] cuts the bottom of his pocket open, and grabbles all his Bit.
c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Grabble. to seize. To Grabble the Bit; to seize any one’s money. Cant.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn).
1811		Lex. Balatronicum [as cit. 1788].
1823		‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 90: Grab (v.) — To snatch; from grabble, probably.
1837		Lytton Ernest Maltravers I 41: I thought he’d have rin [sic] away with it from the counter — so I grabbled it up.
1881		Trumble Sl. Dict. (1890).
1887		Ebsworth Cavalier Lyrics n.p.: Filchers, who grabble at other folks’ chink [F&H].
1897		(con. 1860s) W.E. Barton Hero in Homespun 30: They hain’t time to grabble the ’taters, Jack.
1969		Letter in Edelman Dear America (1985) 13 Aug. 216: The higher-ranking Vietnamese grabble for the rake-off and black market profits.