Green’s Dictionary of Slang

worry v.

SE in slang uses

In phrases

I should worry [Yid.]

I don’t care.

1907		B. Fisher A. Mutt in Blackbeard Compilation (1977) 4: I should worry.
1915		Van Loan ‘The Spotted Sheep’ in Taking the Count 95: I got all the insurance piled onto that car she’ll carry [...] I should worry.
1919		Wodehouse ‘Jeeves and the Hard-Boiled Egg’ in My Man Jeeves [ebook] The old boy said that in London the trip would have set him back eightpence; and the cabby said he should worry.
1920		F. Packard White Moll 145: Looks kind of bad for Nicky Viner – eh? We should worry!
1923		Smith’s Wkly (Sydney) 2 June 21/1: ‘If there was a “stink,” he'd have the goods on him, and I should worry.
1925		Wodehouse Carry on, Jeeves 75: The old boy said that in London the trip would have set him back a shilling; and the cabby said he should worry.
1933		J. Spenser Limey 24: But you should worry, Limey. You’ll learn all right.
1957		G. Kersh Fowlers End (2001) 253: But I should worry — eh, Mr. Laverock? I got no money to buy up land.