When you start a new week, if you had entered time from the previous week you will be given an option to copy this data to the current week. By default only the tasks from the previous week will be copied to the current week. But if you are a user administrator you can allow specific users to copy hours and/or comments as well. To do this see below.
If you have the "User Administrator" permission then you can set which users can have the hours and comments copied over from the previous week to the current week. Again by default, when a user attempts to copy the previous week's timesheet it will only copy over the tasks. So by checking the below boxes it will also copy the hours and/or comments over as well.