Green’s Dictionary of Slang

east and west n.²

In phrases

give somone the east and west (v.)

(US) to look someone over, to appraise.

1910		O. Johnson Varmint 14: ‘Doc,’ I says. ‘I wish you’d gimme the East and West [...]’ ‘Just what is the East and West?’ he asks me. ‘Why, look me over!’ I explains.
1917		Cincinnati Enquirer (OH) 12 May 12/2: ‘He gets a hunch tuh go back an’ give the joint East and West’.