Teaser 2993: Baker’s weights

From The Sunday Times, 2nd February 2020 [link]

A baker’s apprentice was given a 1kg bag of flour, scales and weights, each engraved with a different whole number of grams. He was told to separately weigh out portions of flour weighing 1g, 2g, 3g, and so on up to a certain weight, by combining weights on one side of the scales. He realised that he couldn’t do this if there were fewer weights, and the largest weight was the maximum possible for this number of weights, so he was surprised to find after one of these weighings that the whole bag had been weighed out. Upon investigation, he discovered that some of the weights weighed 1g more than their engraved weight. If I told you how many of the weights were too heavy, you would be able to work out what they all were.

What were the actual weights (in ascending order)?

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