The smart-aleck answer is virtually nothing, as in low Earth orbit gravity is nearly zero, meaning the International Space Station has mass but only negligible weight (defined as the force on an object due to gravity).
However, if the ISS were brought down to Earth now, it would weigh around 420 tons – although with so many components bolted on over the years, it’s difficult to be exact.
The first ISS module was Zarya, launched via the Russian Proton rocket on November 20 1998 and was responsible for propulsion, orientation control, communications and electrical power. It weighed around 19,300 kilograms (42,550 pounds). Since then 160 or so modules have been ferried by various US and Russian missions and installed through over 1,000 hours of extra-vehicular activity (ie space walks) as well as operations by the ISS’s European Robotic Arm (ERA).
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