Yeah, those circular metal disks. Weights or masses? I call them weights because when I attach them to a spring I'm interested in their weight, but it feels odd saying a "Pick up the 100g weight". "Pick up the weight with a mass of 100g sounds better" but it still feels wrong.
I don't like to call them masses, because I've never heard anyone else call them masses, unless it's someone trying to correct me for making the 'mistake'.
It is absolutely fine to call these objects "weights", since you are interested in their weight - i.e. the force of gravity on them. You are not using them for their inertial properties.
Dictionary definition of weight: (Dictionary.com - definition 5)
a body of determinate mass, as of metal, for using on a balance or scale in weighing objects, substances, etc.
NB - this definition makes it explicit that a weight has mass. In other words - while you call it a weight (the object), the physical property is mass (100 gram). Which, at a particular point on earth, translates into a weight.
So, even though they are measured in grams (which you correctly assessed as a unit of mass), it is quite all right to call these objects weights. That is because the word weight can refer to the force of mass times acceleration due to gravity or "a body of determinate mass." (dictionary.com)
If you pick up a weight and bring it some other place, then the weight at that other location will not be exactly the same. Wat happened to the difference between the initial weight and the final weight? Because weight it is not conserved, nothing needs to have happened. If you had instead said that you picked up a mass and brought that mass to that other location, then because the mass would be the same, you would avoid this ambiguity.
So, it's better to refer to mass instead of weight, but it does come at the risk of making you look like this guy:
