over the left
(obsolete, slang) Short for over the left shoulder.
A common pickpocket trick is for the operator to carry a shawl or overcoat carelessly over the left arm, and to take a seat on the right side of the person they intend to rob in a streetcar or other vehicle. Harry Houdini
Don't you like this hat?‘ ‘No, sir.‘ ‘Well, I do,‘ I replied rather cleverly, and went out with it tilted just that merest shade over the left eye which makes all the difference. P. G. Wodehouse