Okay, I'm going to pass on commenting about the 6683 net calorie defecate
. Because I really am speechless at that one.
However, I can say for sure that weight gain when you start exercising is not due to muscle building...it doesn't happen that fast, or make that much of a difference, but what may be happening in your case is that with exertion, muscles retain water. That can add to weight. It should stabilize out over time. Additionally, other factors, such as sodium intake or your monthly cycle (provided you're female) can add pounds temporarily).
Also, it is important to remember that just because you have calculated a calorie deficit doesn't mean that you will see a loss that exactly corresponds to that deficit. Several factors influence your weight at any given time, and the measurement of the calories is negligible at best. But it does yield a drop over time.
Hang with it, keep doing what you need to do, and congratulations on your results so far! We'd love it if you stuck around and shared the journey with us. Holler if we can help in any way