I agree with chalup.
My standard carb intake is veg (usually something like salad leaves, coleslaw, green beans, courgette, broccoli, aubergine, tomatoes, cauliflower, mushrooms, peppers, mangetouts, sugarsnaps...) with meat, fish, eggs, cheese. I add cream to hot drinks if appropriate, and about twice a week I have berries and cream.
That is consistently 20g carbs or less a day, and is filling and enjoyable.
However, adding in any processed or 'modern' eating habits will scupper the carb target instantly, and halt weight loss just as fast.
I find that including any grain (even a slice of toast, or a tablespoon of rice) will cause problems.
I also need to drink a lot of water, and take steady exercise (dog walking daily) or my weight won't shift.
It is, I believe, down to the insulin resistance. We each of us have different amounts of insulin resistance, and our bodies respond to the insulin resistance in different ways. For me, and I think for many people who find it very difficult to lose weight, if we have enough carbohydrate in our diet (and for me that is more than 20 g carb a day), then our insulin resistance increases. So we have to produce more insulin to overcome that insulin resistance. Our bodies have to work very hard to do this, and have to produce far more insulin that a normal person would, even a 'normal' T2 diabetic.
So then we have all this insulin floating around. And one of the functions of insulin is to grab every bit of blood glucose that it can, and tuck it away as fat in the cells.
Consequently, even though people may low carb at 40-150g carbs a day, they are still using masses of insulin, and their body is still fighting to use that insulin to put the glucose away as fat.
You can test to see if this theory applies to you by Fasting or doing a 3 day Fat Fast.
OR alternatively dropping your carb intake to 10-20 g a day for a couple of weeks, and seeing what happens. You do need to do it for long enough to use up any glycogen reserves (several days) BEFORE you start seeing the weight loss benefits though.
There is an interesting section in the Voleck and Phinney 'Art of Low Carb Living' book where they discuss this, and state very clearly that for some people (usually but not always women, often middle aged, and often with additional health issues and hormone issues) can only lose weight on regimes of 20g or less carbs a day. And the unfortunate detail that made me very miserable to read, was that the more diets people have been on, and the more 'broken' their metabolism has been by those diets, the more likely it is that these people will have to stay on the 20g regime for a long time. Possibly indefinitely. In order to see the same benefits that other people get from 80-130g carbs a day. Even then, weight loss can be very slow.
Some of us even need to practice intermittent fasting to get the carbs low enough.
I seem to be one of these select few, and it isn't a club that I particularly enjoy being in. But my experiences seem to back up everything that V&P have said.
However - and this is a definite benefit from this 'club membership' - IF you get your carb intake low enough, then your insulin resistance drops, and your glycogen stores are used up, and you are not 'messed up' by insulin resistance, then yes, YOU CAN eat additional fat, and not gain weight.
I have tested this repeatedly, and can eat huge amounts of fat and not gain weight, provided my carbs are low enough.