Why did Anne and her sister most likely wear so many layers of clothing?

They couldn't carry suitcases or else they would look suspicious and would be asked to open them. So they had to wear as much clothes as they could in order to bring it with them. Their father Otto did carry a briefcase of clothes because it was normal and he wouldn't get caught.

I'm guessing you're talking about Anne Frank and it would be because the lived in the attic and it was cold.