I recently got glasses that are thicker than my previous and there was no issue, like they always have been. There are various types of 3D glasses and they all work for me.
Also, glasses stay on for all rides. However, if you feel subconscious at certain points in the ride, in which it suddenly stops, you can press your fingers against the frame if it makes you feel better. However, as much as I've worried in the past when I first went on rides, they always stayed on my face.