Your'e right. You are ignorant, and, not all that coachable.
You cannot gain muscle without gaining weight, because muscle has weight, unless you happen to lose fat at the same time, and the only way you can really do that well is with chemical muscle enhancement.
Muscle is much denser than fat, and muscle burns about 15 calories per 1 pound of it, per day, every day.
If you want to be able to be leaner, stay leaner, and have a higher metabolic rate, you have to increase your lean muscle mass, or muscle mass ratio. In fact, increasing your lean muscle mass is the ONLY way that you can increase your base metabolism, without chemicals, as you grow older. Having more muscle allow you to eat more calories; eating more calories allows you to have more muscle.
Since you're already tiny, the latter (changing your body composition) is not really an option for you. To gain lean muscle / weight you need a surplus of calories which works out to about 15 calories per pound of lean muscle; you need about 600 calories for a moderate workout; you need about 600 calories to grow on.
So, let's say you have 140 pounds of muscle, that would be 2100 calories, JUST TO SUPPORT THE MUSCLE. Now add 600 calories for growth. Add another 600 calories to sustain a moderate workout. Clearly, you're not even getting enough calories to sustain your current weight, much less a vigorous workout routine geared towards metabolic activation and muscle gain, and athletic performance.
I've tried telling you several times, but, you keep defeating yourself in your lack of research, stubbornness, and lack of common sense. If you want a slow metabolism that preserves fat, and sheds muscle, keep doing what you're doing.
The laws of science, and your body work that way. You can continue to NOT listen, and, you'll continue to fail.
When I'm at most lowest fat levels, around 4%, I'll bring my calories UP to over 4000 to sustain my activity level, and 3-a-day workouts.
Eat to win.
In this picture, I'm eating over 3800 calories per day, and working out three times a day. Clearly, you don't need 3800 calories a day, but, you need at least enough to makes gains, or you're wasting your time in your workouts.
Low calories diets, particularly those low in carbs, invoke the feast famine response teaching your body how to becoming a fat-storing, muscle-burning, machine. That's why fat asses so often fail in diet. They just don't get it. They refuse to understand it.
Without gaining some weight, you cannot gain muscle. Without adequate calories you cannot gain muscle. Unless you have a dead on diet, great genes, or use chemical muscle enhancement, you can't gain weight without gaining a bit of fat.
That's just how the human machine works.