To observe. Twig the cull, he is peery; observe the fellow, he is watching us. Also to disengage, snap asunder, or break off. To twig the darbies; to knock off the irons.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
in twig * twissNathan Bailey's 1721 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes