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Feynmann's machines are idealised devices and we don't know or care about how they work internally. All we know is that we can connect the weights to the machines and they will move them according to the rules. The 1kg and 3kg weights start at height zero. We connect them to machine B and it lowers the 1kg weight to $h=-1$ and raises the 3kg weight to $h=Y$....
The answer to your question is, to a minute degree, is yes, since the total energy of something measures its source strength / coupling to gravity. So, if an system has energy $\Delta E$ added to it, it will weigh more - its gravitational mass will increase by $\Delta E/c^2$. Practically, the effect is almost unmeasurable; a magnet's stored magnetic energy ...