Recommended course weight for online quizzes outside of class In many of my classes (mainly with undergraduate students), I begin every class session with a reading quiz, that is, a short, simple multiple-choice quiz on their assigned reading, to make sure that the students have read before class so that I can spend class time on more challenging and interesting topics than merely regurgitating the textbook for them. This counts for around 5% of the course grade. This technique has transformed my teaching, so I want to retain it in principle. However, there are many logistic challenges to administering these quizzes when I occasionally teach large lecture classes of over 100 students (especially Internet connection problems). So, I want to try to move these quizzes to the course learning management system (LMS), due the night before the class session.

My challenge is that I am afraid that many students might cheat and answer questions by looking up the reading material or sharing answers. When I do reading quizzes in class, I invigilate to restrict cheating, but I would not be present during the online quiz. I have researched and plan to implement multiple techniques to limit cheating in online quizzes (e.g. limited answer time; rotating questions for different students; etc.), cheating cannot be completely eliminated. My main concern with cheating (other than students hurting their conscience) is that if they don't read the assignment, then their learning during class next day would be severly limited.

With that background, my specific question here is: what is an appropriate amount of course weight to assign online quizzes that are given before every course session, considering the risk that student cheating might be quite high? For me, giving no course weight at all for these quizzes is not an option--a reading quiz that carries no weight is virtually useless.
My favorite way of incorporating out-of-class online quizzes is rather unconventional.  

Rather than worrying about cheating, we encouraged students to work together and even to keep redoing the quiz until they got everything right. Then we incorporated their scores into their overall class grade as a multiplier.  

In other words, the grade for the class was: grade = weighted_tests * f(online_quizzes)

We played some fancy curving games with that f function to mean that students wouldn't get hurt by being a little off, but that they'd suffer badly if they didn't take the online quizzes seriously.  The net effect was to use the online quizzes as self-grading practice work, with a grading "stick" to enforce that the students were actually expected to do them.