Muscle weighs more then fat, but I also want to lose weight at the same time. I don't have much of a food budget so eating healthier (more expensively) is out of the question.
I'm not sure muscle weighs more than fat, I think its more of an old wives tail.
But after you lift weights then muscles are hurt, hence the pain, it takes a lot of energy to repair them, energy that would otherwise could convert to fat. So weight training helps you lose fat. Throwing in some cardio doesn't hurt either, HIIT works best for me and cuts the time I have to do it for.