Weight stall

Hi,

I am a bit worried about a prolonged weight stall. I am doing the diet with my partner. We started in february. In th first couple of weeks we both lost about 5 kgs (10 pounds) and have been yoyoing kilo up and kilo down since then. We are doing a very clean keto diet and walking almost every day. Some intermittent fasting, usually skipping breakfast. He complains that he feels hungry all the time, but I dont. However, I do feel some heart burn occasionally when eating fat from meat sources. I know that in theory there are no health consequences from the keto diet but i feel increasingly worried about cholesterol and such, eating so much fat and not losing weight. I am using a food calculator with macros, trying not to go over 20 carbs a day (1300 calories for me, 1800 for him). 

Typical breakfast (not every day)

2 eggs (fried or scrambled)

1 sausage or avocado or bacon

1-2 slices cheese

fried peppers or mushrooms or both

Typical lunch/dinner

Some protein source (chicken breast on the pan, oven baked chicken leg skin on, fried salmon, beef), occasionally with cream and full fat cheese sauce

Some veggies (cauliflower mash or broccoli with sauce or mushrooms or small salad)

Or big  salad (tuna, cheese, avocado)

Snacks (not more than once each day, not every day)

Handful of brazil nuts/macadamia/walnut

OR

Creme fraiche (1tablespoon) + full fat cottage chese (2 tablespoons) + 4 frozen berrries + chopped nuts

OR

1square 85% chocolate

OR

olives and cured cheese and meats

I am cooking everything with butter/more oil than usual.

EDIT- He started on 250 lbs (118 kgs), aiming for 200 lbs(90kg), to be able to start doing normal exercise again. I started on 190 (87 kgs) aiming for 150 (68 kg).

We did the dukan 5+ years ago, I lost roughly the same as I intend now and kept it for some years, he lost 60+ but couldnt keep it. We have no health issues (no cholesterol or high glucose or high blood pressure).

We usually take coffe/tea plain, but sometimes add a little full fat cream or non sugared almond milk.

Did some “fat bomb treats” (with edulcorant, full fat cream cheese, almond flour, butter etc) at the beginning (keto cheese cake, keto tiramisu, keto cookies) but nothing in the last 2 weeks (worried about th edulcorant, the only type I could find where i live now)