WARNING: This post will, I think, only be of interest to people who – like myself – only brew small batches of 10 liters or 3 gallons or even less.
I built a small Tilt-style hydrometer (it had to be small to fit the small openings of my small fermentation bottles), but then only used it once. There is something about the idea of having this tube thing inside the fermentation vessel for days on end that turns me off. And I'm not really interested in SG readings every hour or even more frequently.
But out of curiosity, I weighed the fermentation vessel once a day and wrote down the weight, as well as the specific gravity as reported by the hydrometer. Here is a graph of the 10 days:
The blue line is the weights, the red, the SG's; both normalized to run from 1 to 0.
The FG, as measured when bottling, was 1 or two points off for both methods, which is good enough for me. (I made the assumption that the volume of the liquid did not change, which made it possible to calculate the SG every day just using the weight at that time. I had weighed the bottle and the airlock at the beginning, so subtracting that sum gave the net weight of the liquid.)
So I gave up on the hydrometer and have been weighing my batches since then – fifteen of them. The error has remained small enough.