If I wanted to ask somebody how much weight he/she has lost, which of the following sentences would be correct:

1. Wie viel haben Sie abgenommen?
2. Wie viel Körpergewicht haben Sie abgenommen?
3. Wie viel Kilogramm haben Sie abgenommen?
4. Wie viele Kilogramme/Kilos haben Sie abgenommen?

Also If I wanted to ask about the period in which they lost the said weight, i.e. whether they lost it in three weeks or two months or one year etc., what should I say? Let's say they lost ten kilograms, can I say:

Über welchen Zeitraum haben Sie 10 Kilogramm abgenommen?

I would be expecting an answer like "in drei Wochen / in zwei Monaten / in einem Jahr ..."

When we look at statements dealing with loosing weights, it might become clearer, because some of these statements could be answers to your question:

Ich habe abgenommen. Sie haben abgenommen.
I have lost weight. You have lost weight.

This is the usual way to talk about loosing weight. The amount of weight is just an option in such a statement. And other than in English you even don't need to use the word »Gewicht« (weight) in such a statement. So, when you ask for that amount you don't need to name this amount in the question and you don't need to use the word »Gewicht«:

Wie viel haben Sie abgenommen?
How much weight have you lost?

This is the best and most often used version.

But of corse variations are possible:

Ich habe 10 Kilo/Kilogramm abgenommen. Sie haben 10 Kilo/Kilogramm abgenommen.
I have lost 10 kilos/kilogram. You have lost 10 kilos/kilogram.

• sidenote
Note, that in German the plural of the unit Kilo is also Kilo and the plural of the unit Kilogramm is Kilogramm. The plural forms Kilos and Kilogramme exist, but are used for weighting pieces that you can pick and put on a weighing pan.

Mit dieser Diät purzeln die Kilos nur so herunter.
With this diet, the kilos just tumble down.

What metaphorically tumbles down in this sentence are not units but weighting pieces.

When you create a question from the statement I discussed before, you'll get this:

Wie viel Kilo/Kilogramm haben Sie abgenommen?
How many kilos/kilograms have you lost?

This is the version that best fits to your options 3 and 4.

Your option 2 is grammatically absolutely correct, but also absolutely unusual. It sounds like a weak translation from English, where you need either the word weight or a unit like kilogram. But German works best without these words.

Über welchen Zeitraum haben Sie 10 Kilogramm abgenommen?

Yes, this is possible and correct. Another option is this:

In welcher Zeit haben Sie 10 Kilogramm abgenommen?

But in my personal opinion this sounds better:

Wie lange haben Sie gebraucht, um die 10 Kilo abzunehmen?
How long did it take you to lose the 10 kilos?

The definite article »die« before »10 Kilo« assumes that you already talked about this amount before. If this amount was not mentioned before, the phrase »10 Kilo« is indefinite, so you need the indefinite plural article, but the indefinite plural article is the null-article, which just means, that you use no word at all as indefinite plural article. (This, btw. is also true for English.)

• Many thanks for the detailed answer! If I may ask: You said at the end of the first paragraph that «Wie viel Kilo/Kilogramm haben Sie abgenommen?» is the version that best fits to my options 3 and 4, "which both are incorrect" ... but my 3rd option «Wie viel Kilogramm haben Sie abgenommen?» is literally the same as the sentence you gave! Sep 9, 2022 at 19:51
• Also regarding «Wie lange haben Sie gebraucht, um die 10 Kilo abzunehmen?» I don't think I can use this if I were a doctor asking a patient about the period in which he lost 10 kilograms (due to some unknown illness), right? Sep 9, 2022 at 19:54
• @KeNSmilePachI: Sorry, I edited my answer now. You are right, your #3 is correct, I made a mistake. About »Wie lange haben Sie gebraucht, um die 10 Kilo abzunehmen?«: You can use this whenever the person has lost the weight voluntarily and with some effort. So if the patient has made a weight loss diet, and was successful, then the doctor can also ask in this way. But if the weight loss is an undesirable consequence of a disease, it is better to ask, »In welcher Zeit haben Sie die 10 Kilo abgenommen?« Sep 10, 2022 at 6:42
• @KeNSmilePachI: Another topic: Note, that in German German and in Austrian German the guillemets are pointing »inwards«. They are pointing «outwards» without space in Swiss German and « outwards » with space in French (but not in Swiss French where you don't use spaces). Becasue only about 5 million people use Swiss German, but more than 90 million use German German or Austrian German, its best to let them always point »inwards« in an international context, like here on German.stackexchange. Sep 10, 2022 at 6:50
• The plural "Kilos" is used quite often in respect to body weight. While nobody would say "Er hat drei Kilos zugenommen" (which would be wrong), it's very common to hear something like "Sein Problem sind die Kilos am Bauch." or "Seit ihrer Atkins-Diätumstellung schmelzen bei ihr die Kilos.", and this has been in use for decades. Sep 10, 2022 at 10:24

The usual phrase is 1.

4 is also possible, although the Plural of "Kilogramm" is not "Kilogramme", but "Kilogramm". So it's either "wie viele Kilogramm" or "wie viele Kilos".

Instead of 2 one would say "Wie viel Körpergewicht haben Sie verloren".

3 is wrong, because "Kilogramm" is treated as countable.

• Many thanks to you! If "Kilogramm" in 3 is treated as countable, what's the problem then with using the plural "Kilogramme" in 4? Is it countable in 3 but uncountable in 4? Sep 9, 2022 at 19:01
• Plural of "Gramm" is "Gramm". Sep 9, 2022 at 19:06
• @KeNSmilePachI; he probably confused #3 and #4. It doesn't matter, though, because both your variants 3 and 4 are wrong: It is not "wie viel Kilogramm" but "wie viele Kilogramm". Notice that body mass is not countable but units are. This is just blurred by the fact that the plural of "Kilogramm" is also "Kilogramm". The same in English, where you ask "how many kg". Sep 10, 2022 at 16:21
• @bakunin according to Hubert's answer above »Wie viel Kilo/Kilogramm haben Sie abgenommen?« is correct, but now you are saying that it should be "wie viele Kilogramm", so which one is correct? Sep 10, 2022 at 19:18
• Dass man bei "Körpergewicht" "verloren" sagt, nicht "abgenommen" ist mir neu und leuchtet mir auch nicht ein. Was hat man denn in 1 abgenommen, wenn nicht Körpergewicht? Sep 11, 2022 at 1:33