"Principles" might be the wrong way to put it. More like "understanding habits" if you will.

Atomic Habits is just that, habits. So it'll help you build and break habits.

I made it a habit to eat better and train more. Leading to said results.

If you want what I did specifically, no processed foods (got to the point where I couldn't eat burger king/McDonalds thanks to stomach throwing a fit). A little bit will more or less always be there. But reducing it heavily. Bread (especially in the US) is a good one to avoid, sauces in general as well.

Then it's all about watching the calories you consume. Make sure to be in less than what your body needs and you'll loose weight.

If you want to work out/build muscle as well. Focus on the clean eating, working out and keeping a slight calorie deficit. No need to go too hard. Gotta have energy for the day after.