Distributing integers using weights? How to calculate?

Question

I need to distribute a value based on some weights. For example, if my weights are 1 and 2, then I would expect the column weighted as 2 to have twice the value as the colum

Answer 1

You have to distribute the rounding errors somehow:

Actual:
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Pixel grid:
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The simplest would be to round each true value to the nearest pixel, for both the start and end position. So, when you round up block A 0.5 to 1, you also change the start position of the block B from 0.5 to 1. This decreases the size of B by 0.5 (in essence, "stealing" the size from it). Of course, this leads you to having B steal size from C, ultimately resulting in having:

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but how else did you expect to divide 3 into 3 integral parts?