If you are sailing out of the U.S. that is not the case. If you have the same cabin booked for both weeks you can leave your stuff but you will have to debark and exit thru US Customs and then check in for the next week. Sometimes the cruise line will expedite the process for B2B cruisers. You will have to attend muster drill both times.
52 Carnival: Mardi Gras, Ecstasy X2, Fascination X6, Celebration, Elation X5, Glory X5, Fantasy X4, Valor, Holiday X3, Imagination, Liberty, Spirit X2, Freedom, Destiny X2, Splendor X2, Dream X2, Conquest, Legend X3, Victory, Sensation, Paradise, Inspiration, Magic X2, Triumph, Miracle, Breeze
6 Norwegian: Sky, Jewel, Dawn, Epic, Pearl, Breakaway
7 Windjammer: S/V Legacy X3, S/V Polynesia, S/V Caledonia, S/V Diamant, S/V Sagitta