Is it permissible to measure foods, liquids or other items, or to weigh oneself or some object, on Shabbat?
The Shulhan Aruch (Orah Haim 323) rules that one may not measure or weigh on Shabbat. Measuring and weighing are closely associated with the marketplace, where merchandise is measured or weighed for the purpose of determining a price. It would thus be an affront to the sanctity of Shabbat to weigh or measure, and for this reason the Sages enacted a prohibition against weighing or measuring on Shabbat.
The Sages made an exception to this rule in cases where weighing or measuring is necessary for the purpose of a Misva. Thus, for example, one may measure the water in a Mikveh on Shabbat to determine whether it contains the required amount of water. Similarly, if milk fell into a meat pot, volume measurements may be made in order to determine whether there is enough meat to "nullify" the milk, such that the meat would be permissible for consumption. On Pesah, one may measure the Masa and Maror so that he knows how much he must eat to fulfill the obligation.
Another exception to this Halacha relates to caring for the ill; it is permissible to take measurements for the purpose of administering medical treatment. One common example of this provision is taking temperature: one who feels unwell may take his temperature on Shabbat with a conventional (as opposed to digital or electronic) thermometer. Likewise, a woman trying to conceive may take her temperature on Shabbat to determine the time of ovulation. One may not, however, weigh himself on a scale as part of his weight loss program on Shabbat, as this does not qualify as medical treatment.
If a child is ill and must take a certain quantity of medication, the parent may pour the medicine into a measuring cup to measure the proper amount, and then give the cup to the child to drink. One may not, however, measure the medicine in a cup and then pour it into a spoon or a different cup for the child to drink.
Summary: It is forbidden to weigh or measure on Shabbat, except when this is necessary for a Misva or for treatment of illness. Common cases where weighing or measuring is permissible on Shabbat include taking an ill patients temperature and measuring the water in a Mikveh. Liquid medicines may be measured to determine the proper amount to be drunk, provided that one drinks from the measuring cup itself, rather than pouring the medicine into a different utensil after measuring it.
