What is a category of star systems where you can figure out how heavy the stars are (their masses) ?

Binary systems are the easiest, where there are two stars in a solar system instead of one.

Explanation:

When there are two stars in a solar system, instead of one, the stars orbit each other. Astronomers can measure quite a bit of information about the movement of the stars. This includes how fast they travel around each other and how often they fully orbit each other. From this information, the mass can be calculated. Note that this information can then be used to estimate the masses of other stars that fit the same type of categories in solar systems with a single star.