First off, a pound of muscle and a pound of fat weigh exactly the same, one pound. However, as you can see from the photo above, and these are "5 pound" examples, but I think you'll get the idea, muscle is denser and takes up "less room". So stop justifying your weight, throw away the damn scale. If you have lean muscle you won't have "things" jiggling around!
Resistance training (lifting weights) will build muscle and with a clean and healthy caloric intake you will burn fat and your body will trim and look better. (Not to mention you'll feel better). Your weight may not change drastically, but your body's make-up will. Focus on how your clothes fit, the energy you have and how you feel. Forget the scale and justifying numbers.