> Do [UK] people not weigh themselves in stones and pounds?

Older people, usually yes.

Younger people, more often that not, not. Even at 48 I use Kg for my own weight, but those only a half a decade older more routinely use stone/measurements.

Though there is a sizable range of people who use one unit system by default but have a reasonable intuition of the other.

Unlike some things, there are no legal mandates dictating which set of measures to use for this.

Another difference in weight scales: we don't tend to work with just pounds when we use imperial measurements. When a US TV show gives a weight as, for example, “172 pounds”, many will need to do a little mental arithmetic (this may be subconsciously, not actively calculating but the process delaying understanding) to convert to X stone & Y pounds rather than naturally having an intuition of the weight from the single number.

I'm a paediatrician. No parent has ever asked me for their baby's weight in kg - they are all pounds and ounces. So much so that I can do this niche conversion almost in my head, at least at the start of the day, as we weigh them in kg.