First, please pat yourself on the back for asking this. I think it very much needed asking.
I'll answer the question, but before that I have some observations to offer. They may sound harsh; I would soften it if I knew how.
2 kg (4.4 lb) isn't much of a weight gain. I have my doubts that such a slight gain would be enough to make a lasting difference, and I wonder if you are setting your "ideal weight" too low for your height and age.
I'm also concerned by the fact that you seem to think that a 30-minute meal is too much eating. For many people 30 minutes means a rushed meal, without the time to properly enjoy it.
I also note from another question you've asked that you measure your weight down to a fraction of an ounce, and that you seem to think that 112 lbs is a healthy weight for a 5'7" 16-year-old female. (Again, this sounds rather low.)
So all in all, I can't help but wonder if you have an unhealthy aversion to food and/or weight gain. If you were in the U.S., I would be posting the number to our National Eating Disorders Hotline and asking you to seriously consider calling it.
As it is, I hope you'll consider the possibility that you need more help than a forum like this can give, and I hope you'll research the resources in your country. (I know the UK has such a hotline; not sure about the resources in other countries.)
Obligatory disclaimer: I am not a doctor, and this is not medical advice!
Loss of menstruation is complicated, and scientists are still trying to understand it. They believe there's a minimum body fat percentage involved; in addition, they know that the hypothalamus and the pituitary can contribute to the problem.
As near as I can tell, it's possible that sometimes the glands shut things down when they "think" you don't have enough body fat. It's also possible that sometimes those glands get "out of whack" because of malnutrition. And sometimes it could be a combination of both, with some other complications thrown in.
You really need an experienced health care professional to help sort it all out.