Recommended course weight for online quizzes outside of class
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.