Very cool, Scott. Thanks for that link. That one explains things in so clearly that even I was able to understand. In effect, when you heat a body, even though you are not really adding additional atoms or molecules, but the additional energy imparted makes the object weigh more - so in a closed system containing 1 Kg of water an increase of 100K would increases the weight equivalent to adding 154 trillion molecules of additional weight, even though no additional atoms were injected into the system.
So weight is not just an exact conversion of the number of atoms in a body, there is an additional element of how much energy it has. That energy could be heat (in which case the atoms are moving fast within the system) or it could be kinetic like the object moving at speeds comparable to speed of light.. This weight of an object approaches infinity as the it tends toward speed of light - which gives rise to the theory that no particle can go at the speed of light, without transforming itself into an electromagnetic wave.