What is the English verb/phrase/expression for cheating customers with an inaccurate scale?

I'm not sure if this is exactly right, but there is the expression "to put your thumb on the scale", meaning that you manually push the scale down while weighing something, to make it seem heavier than it actually is.

The meaning has broadened out from the original "grocer's shop" context to apply to any situation where someone in charge of making a measurement deliberately makes the measurement incorrect, in order to gain some kind of advantage.

http://idioms.thefreedictionary.com/thumb+on+the+scale

• A method of deception or manipulation that creates an unfair advantage for the swindler, likened to a merchant holding a thumb on the scale when weighing goods for sale, therefore increasing the weight and price.
  You have to suspect that the casinos have their thumb on the scale when it comes to the slot machines. There's no way you're getting fair odds.

There are a few idioms that talk about this, like putting your thumb on the scale — biasing a measurement or a situation in your favor.

However, since you asked for a single word, then more generally the term for this would be swindling or cheating your customers.

You might refer to it as using false weights.

false weight noun a weight as measured on a shop scales which is wrong and so cheats customers - investorwords.com

This concept can be traced back at least to Biblical times. The following contrasts a false balance with a just weight:

A false balance is an abomination to the Lord, but a just weight is his delight. - Proverbs 11:1, ESV

Here's an example of the term false weight used in the context of a maths test. The setting indicates that the term is well-established.

A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain ... - Sawaal

Short-change:

verb [ T ] also shortchange

1. COMMERCE to give someone back less money than they are owed when they are buying something from you:

The check-out girl short-changed her.

​ 2. to treat someone unfairly by giving them less than they deserve:

The case alleges that the company shortchanged female employees on opportunities for promotion.

How about to give "Short measure"?

Not specifically weight, you see the term used for any deliberately fiddled measurement (Volume, weight, length....).

The OED gives a definition 1 as :

An amount, especially of alcohol, less than that which is declared or paid for. ‘coal users in North Yorkshire are being sold short measures’ ‘the most serious crime is short measure on a pint’

I would use 'Chiseling' here. It's not overly common depending on your part of the world but it is one word and accurate.

to cheat or swindle (someone): He chiseled me out of fifty dollars.

or

to get (something) by cheating or trickery: He chiseled fifty dollars out of me.

This is normally used in the context of slight cheating not outright cheating.

All of these common English phrases could express your situation:

1. Pull a fast one
   • Usage over time
   • Use Example
     
2. (1)Take someone for a ride / (2)take him for a ride / (3)take her for a ride / (4)take them for a ride
   • (1)Usage over time / (2)Usage over time / (3)Usage over time / (4)Usage over time
   • Use Example
     
3. (1)Short-change / (2)short change
   • (1)Usage over time / (2)Usage over time; be careful of this one's earlier entries; 1888 was the earliest I saw where it's used in this context
   • Use Example
     
4. Fudge the numbers
   • Usage over time
   • Use Example
     
5. Swindled
   • Usage over time
   • Use Example
     

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In regards to thumb on the scale, I won't argue its validity or general use, only state that I have not observed its usage in conversation to any recollection. That being said, I think it is self-evident when used and requires no further explanation, nor a history of usage to be considered valid.

All of these alternatives provided above are common in conversational English in America. Fudge the numbers is probably the least used in a modern context but should still be understood by native speakers.

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For American English, I can also vouch for:
fleeced, by Himabindu Boddupall
duped, by justin
shorted, by Yorik

Dupe can often but not exclusively hold the connotation that the deception was a substitution.

A more generic term that covers situations of minor swindling is diddle:

1. informal with object Cheat or swindle (someone) so as to deprive them of something. ‘he thought he'd been diddled out of his change’

   1.1 Deliberately falsify. ‘he diddled his income tax returns’

-- oxforddictionaries.com

Example: Many of my local street vendors diddle the scales.

My grandmother warned of being sold "a pound of thumb" when buying five pounds of meat. I watched the butcher carefully and never saw him doing that. Perhaps my grandmother had better eyes than I did.

Shorted

Merriam Webster

short [transitive verb] 2: shortchange, cheat

This is a drop-and-go term for your example: "I just got shorted by that sneaky vendor!"

For attestations "in the wild" see for example "shorted my order"

To "give short measure" and to "put a thumb on the scale" and to "short change" are all old idioms that can be used literally or figuratively in describing petty commercial frauds..

"Rip off" is a modern idiom that means to "cheat" or to "defraud" but is not specific in how the cheating/defrauding was accomplished.

The first term that comes to my mind is "jipped" being synonymous with "cheated". Unfortunately a quick bit of research revealed that the more common spelling is "gypped" and that the word is a slur against gypsies and the stereotyped tendency to make easy money off of gullible people. Not knowing the proper spelling, I never made the connection.

www.dictionary.com

verb (used with or without object), gypped, gypping.

1.Informal: Sometimes Offensive. to defraud or rob by some sharp practice; swindle; cheat.

noun

2.Informal: Sometimes Offensive. a swindle or fraud.

3.Also, gypper [jip-er], gypster. Informal: Sometimes Offensive. a swindler or cheat.

Usage note: Gyp in the meanings “to swindle” or “a person who swindles” is sometimes perceived as insulting to or by Gypsies, since it stereotypes them as swindlers. However, gyp has apparently never been used as a deliberate ethnic slur, and many people are unaware that it is derived from Gypsy.

I do think it has been used for the type of dishonest transaction described by the OP:

"Jack was back home from shopping at the market where he just bought several apples that weighed 3 kg. But when weighing it with his own scale, it showed only 2 kg. Realizing that he had been cheated, he told his brother: "I just got jipped by that sneaky vendor! I'm going after him now."

(I'm sticking with my original spelling in order to disassociate from the stereotype)

One term that comes to mind is skimming.

The meaning references taking the top layer off something, as in skimmed milk, but would be used in this context to refer to swindling someone by withholding a small amount from what you owe them or not giving them quite as much product as they are paying for.

The most obvious example I can think of for it's use is the kind of financial crime as depicted in the original Superman movie, where the bad guy made his fortune by intercepting bank interest payments and diverting a penny from everyone's account into his own. The theft was barely noticeable on a individual level, but made a large amount of money for the thief.

The first word that came to my head was "duping".

dupe(verb) gerund or present participle: duping deceive; trick.

Ex: "the newspaper was duped into publishing an untrue story"

Fleecing is a word that is often used in journalism.

Fleece:

Obtain a great deal of money from (someone), typically by overcharging or swindling them.

e.g. The city's cab drivers are notorious for fixing fares and fleecing tourists.

Your sentence could be

I just got fleeced by that sneaky vendor! I'm going after him now.

While this one doesn't necessarily imply an inaccurate scale, it implies the transaction is heavily weighted in one sides favor. If this happened to me, I might say the scales were rigged. Example

The pumps at that gas station are rigged, you don't get your money's worth.

This can also be used in other unfair situations

During his campaign the president posited that the election would rigged against him

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Rigged (verb) past tense: rigged; past participle: rigged

• manage or conduct (something) fraudulently so as to produce a result or situation that is advantageous to a particular person.
• cause an artificial rise or fall in prices in (a market, especially the stock market) with a view to personal profit.

To rig an election; dictionary.com fails pretty hard core on this one. You could also say one is fudging the numbers though that is more of an idiom.

Jack was back home from shopping at the market where he just bought several apples that weighed 3 kg. But when weighing it with his own scale, it showed only 2 kg. Realizing that he had been cheated, he told his brother: "I just got ____ by that sneaky vendor! I'm going after him now."

To answer the original question!

Here are some words to put in the gap.

scammed

ripped off

swindled

overcharged

Note that these don't specifically refer to weight but, if your brother sees you weighing goods and then you say any of the above, your brother will know from the context what you mean!