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.
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.)