SOME QUICK THOUGHTS:
Muscle weighs more than fat. Also increased muscle mass affects calorie burning in a positive way. When increasing muscle mass, you can/will decrease fat. Yet you can still gain weight. A better barometer of success while building muscle and burning fat is how your old clothes fit you.
Body building while expecting to lose weight for the sake of losing weight only is somewhat diametrically opposed. The two ways to reach your goals (as I understand it from your post) is to reduce body mass by losing fat and then, after you hit your weight loss goals, start building up your body mass by building muscle.
OR you can work out your muscles while simultaneously trimming fat and having a restricted/controlled diet. I wouldn’t call this way “body building” because your not loading up on calories to body build per se. Instead, you are controlling and limiting what you eat while toning and developing muscle. High reps are used here.
Body building tends to involve massive amounts of food and typically heavy weight lifting with low reps per set. Pushing maximum weight to exhaustion.
This is just my late night brain storm spatterings based on my past experience. Hope this helps.
ADDENDUM: Decades ago there was a school of thought that a weight loss plateau was due to one’s body metabolism adapting to a routine. The thought was to change up the workout routine so that the body would essentially be “thrown off.” This school of thought worked for me in the past. However there may be disagreement here. I haven’t kept up with the latest research.