There is no scientific evidence that shows that wearing a bra to bed will cause your breasts to sag. Actually, doctors often recommend wearing a sports bra to bed because they are comfortable and supportive if you have large/heavy breasts.
Also, wearing a well-fitting bra during the day is very important too! It’s a good idea to get fitted for a bra by a professional. This service is often free at large department stores that sell bras. Having a well- fitting bra will provide support and likely lessen discomfort that is associated with large/heavy breasts.