Fat and muscle are two totally different tissues. Your bones don't turn into fat, your muscles don't either
Lifting will NOT make you bulk up. It just won't. (Unless you're on a highly strenuous routine with a trainer.) It WILL give your muscle tone, boost your metabolism (not a ton, but a bit!), and keep your hearts, joints, bones, and muscles strong. It WILL protect your muscle from being lost as you lose weight (because weight loss does not just mean you lose fat- it can mean you lose muscle unless you incorporate strength training and good protein sources/amounts into your diet).