Dialogue of a movie, USA, 1955:
Matt: Do you think I can get her drunk enough to sign without reading the papers?
Angie: Let Marge to me.
Matt: What if Marge gets suspicious about you slippping her drink?
Angie: She won't get suspicious. I'll handle light. You get the papers and I'll get her signature.
What is the meaning of "slipping her drink" in this context? Does it mean "encouraging her to drink"?
I am sure he says "slipping", not "sipping". And they are not going to slip any Mickey Finn in her whiskey, they just want to try to get her drunk to be sure that she doesn't know what she signs.
That makes no sense. It must be a bad transcription.
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slip someone something is an expression meaning give someone something surreptitiously.
I don't know your context, but maybe they are slipping her alcohol by secretly adding it into her tea.
drink often means alcohol.
This is real 1950's-era cutting-edge slang. There are three examples in it which is no longer heard today: "Let Marge to me.", "...slipping her drink", and "I'll handle light." "Slipping her drink" means "continuing to push drinks on her."