I think that you are on Moodle 2.2 perhaps .
When you create each feedback instance within a course, you may be able to save the questions as a template and reuse the same template once per weekly instance. Using feedback, it is very easy to not share the results with other students. Perhaps it will take you fewer clicks to duplicate each one using the x2 icon in editing mode.
The other way I can think of this at the moment is using ForumNG, there is a study advice option that would allow a per-pupil-per-week comment giving feedback. with only the teacher and that student being able to see it.
It does sound also a little like a journal application but not sure what sort of feedback you are seeking each week.