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Hank telling to Andy that he wants to knock down a jewellery shop:

Hank: Well, you need money. So do I. Let's solve it.

Andy: What are you talking about?

Hank: Well, there's a place we can knock off. Know it like the back of our hand. Easiest money you'll ever get.

Andy:: What are you saying?

Hank: It's worth about 600 grand. And it's insured, so it's a victimless crime. I offer that in case your faggoty little conscience bothers you. I weigh it off on 20 cents on the dollar. That's 60 grand each. Give or take.

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    "Knock a place off* means to rob the place. "At 20 cents on the dollar" means at 20% of its value. Why the stolen goods are "weighed off" is not clear. Is the thing they're stealing something that is sold by weight? – The Photon Aug 16 '17 at 3:15
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Two steps:

  • "X cents on the dollar" - you will get only X cents per dollar worth of something, see What does it mean to “pay X on the dollar”?

  • "I weight it off" - I cannot find a definition, but from the context, Hanks approximates how much they can get: "I guess" or "I weight it in my mind and I think that..."

Summary: Hank expect that they can sell robbed jewelry at 20 cents per dollar.

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It seems like the expression "to weigh off" is referring to old-fashioned (weighing) scales, where one would determine the weight of something by "weighing it off" with a series of small weights - i.e. placing weights of various quantities on one side of the scales until the weights balanced, then recording the value of the weights placed.

old weighing scales

Therefore, we can deduce that "to weigh off on x" means "to be measured as x". In this case, I interpret

I weigh it off on 20 cents on the dollar.

as

I measure [the amount of money we'll get] to be 20 cents on the dollar [i.e. 20 cents for every dollar, or 20% of the original net worth].

FYI, this isn't exactly a common idiom in modern-day English (I'm a native speaker, and this is the first time I've heard it, so I don't know how much credibility that gives me... :P)

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