I typically empathize very strongly with whatever I'm writing, to the point where I might even experience some of the same physical reactions that my characters are having—tensing up when my character is anxious, etc. There have been times when I was so overwhelmed after writing certain scenes that I needed to take a break afterward, lol.
In spite of this, I don't cry very often while writing, for whatever reason. It has happened a couple of times, one of which being because what I was writing was a little too relatable. 