I found it didn't take long for the weight loss to show up, I lost the first week.
I've been on a lower carb diet (80 carbs or less) and lower calorie diet. (1300 or less). Most days I'm under these targets, the only one I've gone over is fat 46g and I not to do that often as I want to lose weight.) I lost 3.96 lbs the first week, 4.19 lbs the second and 2.43 lbs this week. Bear in mind that I may be quite a bit heavier than you, I started at 273.59 lbs, now 263.01. (if your starting weight is higher, you lose more than someone with a much lower starting weight.) I've also heard that the weight loss is most dramatic on the first several weeks.
I'm counting both carbs & calories, I use an app called Carb Master on my Smartphone which makes it very easy to count them, you set your own goals and you can scan/custom input foods. It also counts water consumption, weight and exercise (the registered version will do blood sugar but I don't test blood.) I've starting exercising 5 days out of 6.
I hope to bring my a1c levels down as I tested at 7 in my last blood test (my other tests were normal). My doctor advised me to lose weight, eat fewer carbs, more nonstarchy vegetables and exercise. (In this part of Canada, you don't get the diagnosis with a single hb1ac test, it takes 3 tests over 1 year.) I'm hoping to avoid a diagnosis of type 2.