I doubt that anyone's weighed a nuclear reactor while operating (which would be quite a feat given their massive mechanical and civil structure); however, operators of nuclear-powered submarines might be able to tell you if any odd changes in buoyancy have been noticed when their nuke plant is switched on or ramped in power.

If we could weigh a reactor with sufficient accuracy, however, science tells us that it would probably weigh less while operating since mass is being converted to energy, and energy is leaving the reactor all the time through leakage.

On a much smaller scale, we have indeed "weighed" the individual components of a nuclear reaction, before and after, and have observed that the reaction products do have less mass than the reactants, as explained by Einstein's famous E=Mc^2 relationship.