Green’s Dictionary of Slang

Grecian v.

[? SE Grecian bend, ‘an affected carriage of the body, in which it is bent forward from the hips’ (OED)]

(W.I.) of a woman, to walk in a self-consciously ‘stylish’ manner, either arrogantly or proudly.

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[WI]cited in Cassidy & LePage Dict. Jam. Eng. (1980).