What should be used to refer to the weights that can react with or displace one gram of hydrogen?

The term that should be used to refer to the weights that can react with or displace one gram of hydrogen is "equivalent weights." This concept is derived from the definitions used in stoichiometry and chemistry, where the equivalent weight of a substance is the mass of that substance that can combine with or displace one mole of hydrogen atoms (or one gram of hydrogen). This term is critical in understanding reactions and stoichiometric calculations, particularly in acid-base reactions and redox reactions.

Equivalent weights help in determining how much of a reactant is needed to fully react with a specific amount of another reactant, thereby allowing for accurate calculations in laboratory and treatment settings. The concept of equivalent weights is foundational in water chemistry, especially for water treatment operators who must manage chemical dosages that are based on the specific reactivity of compounds.

In contrast, the other terms such as mass weights, standard weights, and relative weights do not specifically convey the idea of weight relating to the displacement of hydrogen in chemical reactions. Therefore, they do not fulfill the criteria established by the question, making "equivalent weights" the most appropriate choice.