"Její hmotnost je přibližně šedesát kilogramů."
Translation:Her mass is approximately sixty kilograms.
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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".
I am native AmE. While I can't say "for certain" that přibližně does not mean "nearly," I haven't seen that translation so far.
Even in English, "nearly sixty kilograms" is not the same as "approximately sixty kilograms." To me, "nearly" has an almost-but-not-quite feel to it -- in other words, "somewhat less than" sixty kilograms -- while "approximately" suggests that the actual weight could be either somewhat less, or somewhat more, than sixty kilograms.
Yes, as BoneheadBass says, the meaning is different.
"přibližně" is a little more or a little less, while "nearly" is only less (almost, approaching the value).
"přibližně" is even constructed the same way as the (Latin based) "approximately", where "blízký" is "near/close" (proximus, proximal), and "při-" is the same prefix as "ad-" (realized as "ap-" here), meaning "near" (or "at"), this gives us a double sense of "near", i.e. "near the vicinity of" :-)
"nearly" translates as "téměř" in Czech, and the less formal "almost" to "skoro".