Translation:Her mass is approximately sixty kilograms.
That is true, for example when speaking about a fridge or any other thing of feminine gram. gender. Did you report?
Who says "her mass" when you speak about people, you would say "weight"
"Weight" is also accepted. But I would say that, in English, "weight" would be much more common, especially when speaking about a person or an animal.
This does not have to be "says", it could be a written sentence. It could be from a scientific article, for example (especially in physics, chemistry or engineering). Also, we do not know it is about people. It could be a boat (though one uses "weight" for them in the common language as well).
A question following from your very helpful explanation: If její here refers to a grammatically feminine noun, rather than to a female person, wouldn't "its" be the more likely choice for the English sentence? Of course, that might raise other issues...
I wanted to avoid that so I offered a boat as an example. But yes, if it is a physics exercise and we are speaking about a sphere (koule) or some other object, then we would use "its", so perhaps we should accept it.
I will just add that here hmotnost is the more "scientific" term in comparison to "váha", which is colloquial. That's why the author of the sentence may have preferred "mass" instead of "weight".