OP I am a recovered anorexic so I do know the mindset very well. I had an active eating disorder for fifteen years.
In my case, my eating disorder was triggered by my parents divorce and following that by being treated differently to my brother based on our different body types. I was served different snacks to my brother and in my young mind his were the 'good' snacks, the ones children are often rewarded with, so he was rewarded for his body and I was punished. It took years to break out of this - I urge you to be very cautious and talk through this with a therapist (and if you aren't seeing one, I'd recommend it)
When I had children I had to work very hard on my attitude to their food and bodies. In a way it was easier for me because my children are naturally very slim, it's just how they're made. I do think maybe I would have struggled with them gaining weight, not because I would have minded 'chubby' children, but because navigating managing their weight could have triggered those old thought patterns.
Kids do come in different sizes. Many of my friends children eat well but are bigger, different humans just naturally have higher or lower default weights I believe. In a way having my 10 year daughter has helped me understand that because she is so slim, on the edge of underweight, but eats a huge amount of food and is in fine health - just how she's made. For years I battled with how I was made, and that's where it all went wrong.
Saying all that 4kg is a lot heavier than her brother. What is her actual height and weight? Could it be that actually her brother is a lot smaller than average and she's fine? I think it's worth being really honest about what you're struggling with. Is her weight actually unhealthy, or are you programmed to see it as unattractive? If it might be the latter, you need to work through this yourself. I'm sure you have suffered as I have. You have a duty to stop that cycle from continuing. I was the third generation ED sufferer in my family and I always keep in my mind that I may not be a perfect parent but I will be the LAST in the cycle.
Practically, I would not restrict snacks, but I would restrict open access. She doesn't need to be going into the fridge at 3 and taking cheese and meaty snacks (not sure what those are but sounds like processed meat, be careful of salt content for a 3 year old) I've never allowed my children free access to anything but the fruit bowl but if they're hungry they can ask and I feed them. Constant hunger would have me looking at the meals to see if they're balanced enough.