On the discomfort side, couldn’t they have the collection and recording happen in the background? If no other passengers or staff can see the numbers, there’s less of a chance of someone feeling uncomfortable with the process.
The weighing process involves humans, so that wouldn't be possible.
Their average intelligence being what it is, when instructed to have one person on the scale, sometimes it's one, sometimes two, sometimes two and a stroller. Sometimes somehow a horse ends up on the scale and no one really understands how, including that horse.
Unless you check the weight, you don't know what exactly was weighed.