When I was living in the desert I lost my weight.
Indonesians for some reason like to use the possessive here. But there are problems with this. If you include the possessive then it sounds as though you lost something that you own.
Of course it is possible to own a ‘weight’ (countable thing – definition 1, items 2a and 2b), but not many people are owners of a single ‘weight’, and it’s unlikely anybody would worry about losing one!
If you’ve been living in a desert then it’s possible that you have experienced weight loss (weight uncountable – definition 2), and so if you’re talking about body weight, you need: