You should be "lifting weights"

You're probably here to lose weight. Congratulations for getting started on your journey!

As you know, or maybe you're realizing, you lose weight with a calorie deficit, by eating less than you burn. You can do that without any exercise at all if it suits you, because you burn calories breathing and thinking and going about your day. But if you're losing weight, it's because you're in a deficit.

While you're in a sustained deficit, you're almost certainly going to lose muscle. It's ok, it happens to everybody, and you're going to be much better off for this. But you'll lose a lot less muscle if you use them during this process. That's important because you'll look and feel better on the other side of this, life will be easier, you'll have a slightly better metabolism, and everybody will be crazy attracted to you.

"Lifting weights" won't bulk you up. Building muscles is a type of weight gain, and you have to eat for it. But you're eating to lose weight. So you'll lose weight, mostly fat, you just won't lose as much muscle with it.

I keep putting "lifting weights" in quotes because you don't have to go to a gym, or pump iron. You can use your own body weight, like pushups do. You can use giant rubber bands (called resistance bands). You can do this at home if you prefer, although the gym is a great option too, if you're the type of person who'll go to one.

There are lots of great programs out there. If you have access to the equipment, StrongLifts is a popular (and free!) one. There's also StrongCurves and New Rules of Lifting for Women. On the other end of the spectrum, there are plenty of great videos on YouTube, Fitness Blender, and elsewhere around the web to show you how to do specific exercises and entire routines, with the stuff you have. A set of resistance bands costs about $15 and doesn't take up much space at all.

In short, it's very doable, and it's worth doing.