The Flying Circus answer must have related to the steady flow regime.
During that time the center of mass of a cylindrical hourglass will
be falling at a constant speed. Since the hourglass is not accelerating
during that time the weight will be the same as the weight with no sand
flowing. There will be transients at the beginning of flow and the end
of flow, and your student should examine the behaviour of the scale
during those transients.
My copy of TFCoP is at school or I'd check Jearl's answer. A few of his
answers are not quite right. My explanation (the descending, non
accelerating center of mass) works for me.