Mr. Frank. First let us take off some of these clothes. (They all start to take off garment after garment. On each of their coats, sweaters, blouses, suits, dresses, is another yellow Star of David. Mr. and Mrs. Frank are underdressed quite simply. The others wear several things, sweaters, extra dresses, bathrobes, aprons, nightgowns, etc.) Why did Anne and her sister most likely wear so many layers of clothing?

They could bring into hiding only what they could carry.

Explanation:

In her diary, The Diary of A Young Girl, Anne Frank describes about how they went into hiding.

In her diary entry dated July 8, 1942, Anne first mentions of going into hiding. The Frank family had to go into hiding because there was a call-up notice. In her diary entry dated June 20, 1942, Anne describes the conditions Jewish were going through during the time of War. She states that Jewish were required to wear a yellow star when they go out, were forbidden to use streetcars, even ride their own cars, forbidden to be on streets between 8 PM to 6 AM, etc. As there were so many restrictions and with the call-up notice, the Frank family had to move quickly into hiding before they were forcefully taken into concentration camps.

Since there were so many restrictions on Jewish, they could not carry big luggage. So they wore layers of cloth that they will be taken into hiding. They wore layers of clothes because they will not come back to take more luggage thus they could bring only what they will carry.