“I don’t want to get big.” Lol. It’s not going to happen. This tiny woman does weighted pull-ups with half her bodyweight (video here: https://www.instagram.com/p/B-CRp2GD6IM/). She’s at least 50-100lbs lighter than the average non-lifter. If you lift, you get stronger. If you're stronger, you burn fat while doing NOTHING. If you're stronger, you can perform sprints at an intensity which burns a pound of fat every hour or so. If you're weak, you will absolutely never ever ever burn any significant amount of body fat.
The average woman in the US weighs 170lbs. I’ve been in the fitness industry for 16 years hearing skinny fat and obese woman say they don’t want to lift weights for fear of getting big. Meanwhile, I’ve watched women lifters explode in strength while reducing body mass.
The laws of physics apply to you regardless of your sex or your idiotic beliefs.