Me neither. I suppose it is technically wrong to say "A scales", but I think of it as shorthand for a set of scales, or a pair of scales. Modern weighing machines aren't literally sets or pairs, anyway (like the Libra sign of the zodiac, or those held by Justice). Yet to say "a scale" (singular) just sounds wrong. If it were possible to weigh oneself on the moon, I'm sure one wouldn't use classical scales anyway.
American English uses singular "scale," to indicate a singular object used to weigh something, usually flat so it can be stepped on or such. A bathroom scale, a food scale, a luggage scale, etc.
Wegen is to measure the weight of something. Afwegen has the same meaning, but it can also mean to consider (options you have).
Afwegen, in addition to what Susande says, also is typically used when you weigh and take something, for example when weighing flour while cooking. I think that "weigh and put aside" would be also correct for afwegen.
But not your weight. The sentence is absolutely correct from a physical point of view.
The confusion rises from using kilos as a unit of force, which makes sense only on Earth, where a 1Kg mass weighs 1Kg as a unit of force. So the answer is no, a scales actually measures Newtons, the proper unit of force. On Earth a 1Kg mass weighs 9,81N, on the Moon much less.
Well, it depends on the scale. Some scales use a reference weight, and those will show the same value in kilograms on the Moon. The scales you're taking about are actually dynamometers in disguise. They'd show a different value in kilograms on the Moon, but that would be a wrong value.
No. On the Moon that medical scale would show the right value, in kilograms, pounds, stones or whatever, of your mass, but NOT the right value of your weight. On the other hand, a dynamometer marked with kilograms would give you the right value of your weight in kilograms, but NOT the right value of your mass. We aren't by any means splitting hairs, I am correcting a wrong statement of yours.
You're right in the first part if you are speaking about a pair of scales, like that of the "blind justice" image. Only I would say that they use a reference mass. In the second part, a dynamometer (a bathroom scale for instance) would show the right value in kilograms as a unit of force. Of course it would be a wrong value as a unit of mass. Anyway, the sentence "(on a scale) on the moon you weigh less" is correct.
Also, a pair of scales doesn't show any value, it only shows that two objects have the same weight.
I was thinking more of something like this: http://www.scalesgalore.com/global/images/product_2/493/4933_250X250.jpg
That would also show the correct amount of kilograms on the Moon. A dynamometer that's simply marked with kilograms instead of Newtons (which is what most bathroom "scales" are) would give the wrong value.
But anyway, we're splitting hairs here. My initial comment was meant more like a joke. The sentence works for what it was meat to do: teach Dutch.
The kilogram is a unit of mass. That's what it measures, nothing else. Don't believe me? Wikipedia is your friend. It does not measure force. The unit for force would be Newton. The word "weight", when referring to a person is synonymous to "mass". The force that draws objects together by virtue of their mass is called "gravity". You probably wouldn't say "look how much gravity the Earth is exerting on that person, and vice-versa". If you did say that, then of course it would make sense for the value to be different in the case of the Moon since the Moon itself has a smaller mass and therefore a shallower gravitational well.
An instrument that displays a value in kilograms is an instrument that is supposed to measure mass (since that is the measure the kilogram is a unit for). An instrument that is supposed to measure mass, but shows different values for the same mass depending on circumstances (ie: whether the mass is on the surface of Earth or on the surface of the Moon) is an instrument that is measuring the wrong way.
But by all means, feel free to correct my wrong statements. :)