Welcome to the daily halacha (Jewish law). Can one weigh themselves on a scale on Shabbat? So, we know Maran (our master) HaShulchan Aruch discusses in Siman (section) Shin Vav (shin and vav), among other places, how Mekach U'memkar b'Shabbat is not allowed, which means a person cannot do business on Shabbat. That includes many, many, many things. It branches out to different things. It's not only about sales and buying, which are not allowed on Shabbat, but also things that may lead a person to write, write checks on Shabbat, write signatures on Shabbat, or touch muktzeh on Shabbat, which is money. So anything that applies to these things is not allowed. One of those things is measuring on Shabbat. A person cannot measure on Shabbat.
Halacha lema'aseh (in practice), a ruler, for example, is muktzeh on Shabbat. A regular ruler that we have in our sukkah (temporary hut), in our backpacks, at school, or on our desk is muktzeh on Shabbat. A scale is muktzeh on Shabbat. We're talking about scales that are not electronic. If they're electronic, they're definitely not allowed to be used on Shabbat. But even with a scale that's not electronic, a person is not allowed to weigh themselves on Shabbat. Maran Chacham Ovadia himself says that if a person wants to weigh themselves on Shabbat, they should not use a scale, even though it's not electronic.
However, in a case where somebody is very old or a child who's not well, chas veshalom (God forbid), and the doctors are saying that they should weigh themselves after every meal to make sure they're healthy, in a case like that, we already consider it tzorech mitzvah (mitzvah-related need). So then they're allowed to weigh themselves on a scale that's not electronic. But any other person, Halacha lema'aseh, cannot weigh themselves on a scale on Shabbat. That's why a scale, even though it's not electronic, will become muktzeh on Shabbat.