There's a video of assembling a physician's scale here.
And here's a photo of the bottom:
I estimate that the poise on the scale's weigh beam have a mass or less than $1/1000th$ of the scale's capacity, and there's no minimum weight for the scale, so the scale must have an mechanical advantage of at least $1000$ between the end of the weigh beam and the platform.
This could be achieved with three levers in series, each with a mechanical advantage of $10,$ or two levers each with a mechanical advantage a little over $30,$ or some other combination.
I see that the weigh beam is one lever, and that it's in series with the long lever under the scale. The load from the platform seems to come in at these places (green arrows):
It looks like the long lever has a mechanical advantage of about 18; I measured 47 pixels and 828 pixels for these two distances (green):
If the mechanical advantage is just the long lever in series with the weigh beam, that would leave the weigh beam to have a mechanical advantage of more than $50.$ Is that right? Perhaps there is some mechanism inside the horizontal crossbar beneath the weigh beam giving part of that mechanical advantage?
My guess was that the short lever is not adding mechanical advantage, but instead positioned so that it doesn't matter whether the patient stands near the front of the scale or near the back. Is that right, or is the short lever needed for additional mechanical advantage?