Line widths are specified in points (1/72"), not pixels, and locations on a plot are expressed in the same units as the axes. When displaying a line on your screen, the computer must "convert" these values into pixels. The problem is, pixels are discrete: you can't use only part of a pixel.
So, for example, 1 pt might correspond to exactly 1.4 pixels (I'm making these numbers up, but hopefully you get the idea), and the location 6.3 on the vertical axis could correspond to 300 pixels up from the bottom of the figure, while 6.4 corresponds to 303.2 pixels from the bottom.
To plot the first line, the computer wants to draw a line across the figure, with the vertical location of the bottom and top of the line given by 300 and 301.4 pixels from the bottom. But since you can't draw part of the pixel, the computer rounds these numbers to 300 and 301. Thus, the first line is 1 pixel wide.
On the other hand, the vertical location of the bottom and top of the second line is suposed to be 303.2 and 304.6. In this case, the computer rounds to 303 and 305: a 2-pixel-wide line.
Note that this becomes less of an issue if you either display the figure in a higher-resolution setting (e.g., if you print it on a printer, which should have a much higher resolution than your screen), or if you make your figure significantly larger (e.g., maximize the figure window).
