Q. Is it permissible to keep a mechanical (non-digital) food scale next to the table on the Seder night to measure the appropriate amounts of Matzah and Maror for all those present?
A. Shulchan Aruch 306: 7 rules that our Sages forbade measuring or weighing anything on Shabbos or Yom Tov, for these acts resemble the weekday actions of merchants conducting business. However, one can generally do so for the purposes of a Mitzva (Shabbos 126b). For instance, one may measure a Mikveh on Shabbos in order to ascertain whether or not it is lacking water.
Poskim therefore write that it is permissible in need to weigh Matzo and Maror on Yom Tov or Shabbos (when the Seder night coincides with Shabbos). Chazon Ovadia- Shabbat, Volume 6, page 26 and others. The above applies only to a mechanical scale, not a digital one.

Horav Shlomo Miller’s Shlit’a opinion as explained by Horav Aharon Miller Shlit’a is that all measurements and weighing should be done before Shabbos and Yom Tov.

Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a