Heating a cylinder full of water on a scale does not change its weight significantly, as the mass remains constant despite the introduction of energy. While heating does cause the water to expand, this expansion may result in a slight buoyancy effect that could make the scale read a bit lighter, but this would be negligible. The energy added through heating is minimal in terms of mass change, requiring an impractically large amount of energy to register on a scale. Additionally, convection currents in the air around the cylinder might affect the scale reading, but the overall weight remains unchanged. Thus, the weight of the cylinder and water is essentially constant, ignoring any relativistic effects.