Martin - that all makes complete sense as a way of refining the process, but I still find I can't hit 128 exactly, even with very high zoom levels. I wonder if this is because although we can 'see' sub-pixels, they don't really exist (at 100% zoom), and furthermore (because of the nature of pixels, as discrete entities) its hit and miss as to whether we can ever hit a mid point. Consider the case of a 1 x 9 pixel line: the mid point is 4.5 pixels, but 4.5 can't exist, so the dividing line has got to be between either pixel 4 and 5 or 5 and 6.
That said, I think the accuracy I am already able to get (within a fraction of 1%) is good enough, and probably less than other inaccuracies eg the real yacht's lines are traced digitally by hand from old drawings that were themselves not always 100% perfect, and the old time way of doing the test for the mid-line (balancing a stiff paper cut-out of the section on a knife edge) was itself prone to minor errors eg marking the paper where the knife edge had been, and even the width of the pencil line itself. The digital method also makes it very easy to be sure the line is perpendicular to the waterline, which matters because what we are really interested in is the centre of buoyancy. If the paper method produced a line that was not exactly at 90 degrees to the waterline, then, depending on where the measurement was taken, another source of error could creep in (the line would still pass through the centre of balance/buoyancy, but the line's distance from say the centreline would vary with height, and would only be accurate at the (unknown) vertical height of the centre of buoyancy, which was not determined according to surviving written descriptions of the old time methods).
One of the useful things about doing this digitally is we can always go back and recheck if need be, whereas in the old days the paper cut-outs would probably have been discarded once they had been used.
For anyone who wants to research the method further, it's usual name is Turner's Metacentric Shelf theory. Rear Admiral Turner, as he became, was primarily interested in designing balanced model yachts, but his thinking became incorporated into full size yacht design for a while, notably by Harrison Butler, and his book 'Cruising Yachts: Design and Performance' (1945) contains a detailed (though it has to be said not always immediately grasped) description of the method. Interestingly, soon after the method had got established, others discredited it, pointing out that it was a hydrostatic model (still hull sitting in still water) and that a real yacht under way is anything but static, and therefore the theory couldn't apply. But for some unexplained reason, yachts that have a good metacentric moment profile (the second part of a metacentric analysis) are generally well balanced, and those that have a poor profile tend to be difficult to handle, so the theory does have some practical use, even if we don't know exactly how it works (my own hunch is that it is because the key part of the assessment is relative, so although the absolute numbers might be wrong, they are nonetheless useful because the relative contributions do reflect reality, if that makes sense).