It is a myth that wearing a bra (during sleep or at any time) increases the risk of breast cancer. There are no data from scientifically sound studies that show any increase in the risk of developing breast cancer from wearing a bra.
This myth may have started with a general observation that breast cancer is more common in Western, industrialized countries where wearing bras is more common than in the developing world. However, to then draw the conclusion that it is the bra-wearing that causes the breast cancer is completely erroneous. Women in developing countries have shorter life spans during which to develop breast cancer and do not undergo breast-cancer screening. It is probably for these reasons that their chances of being diagnosed with breast cancer are lower, not because they are less likely to wear bras.
Bottom line: If wearing a supportive bra to bed allows you to sleep more comfortably, you can do so without worrying about any health risks