You're right.
The mass of an object which consists of many pieces stuck together
depends on the state of motion of the pieces. If you heat up an object,
its atoms jiggle around faster. Metals even let electrons move freely
inside, and a hot metal will have electrons moving more quickly.
Because the component pieces have more energy when they are moving
faster, the total energy of the object is greater. The total energy may
include that of photons too, and so it isn't just the fermions which
contribute. The mass of an object at rest is its total energy divided
by the square of the speed of light. The object will weigh more on a
scale if it has more mass.
If the entire object is moving, it's hard to put it on a scale in
order to weigh it. If the Earth moves along with the object (or
equivalently, a stationary object on a stationary Earth as viewed by a
moving observer), then the amount of force a scale reads remains the
same. If the object flies past the Earth at high speed, then the force
due to the earth's gravity on the object does increase with the speed
of the object, so one can say that in this case it weighs more too.
Mike W. and Tom J.
(published on 10/22/2007)