Matter can be defined as the physical aspect of the world. Matter is also consisted of atoms, molecules, and elements and takes up space. All solids, gases, and liquids consist of various numbers of atoms and elements and thus will take up space to some extent. Thus, one can deduce that if matter takes up space, it has weight as well.
Prions, however, are not living organisms. Prions are infectious proteins. For unknown reasons, these proteins refold abnormally and cause a domino effect in surrounding proteins which in turn mutate into stable structures