I certainly did (and still do)
The most memorable sob moments for me were Mikage's death in 07-Ghost manga and two certain character deaths in Majin Tantei Nougami Neuro manga. It was during the time I felt very apathetic, and I never cried my eyes out because of comic characters before, so yeah. I was surprised I could still feel some sadness, especially because of a fictional character. I didn't even relate with them, it was just that damn sad and unfair for them to end like this.
And then the more manga and anime I've consumed, the more I had to get used to the fact that 80% of my fav characters die in a series :'D
"Hey, wanna know where my fav characters are?" makes a wide hand movement at a graveyard in the distance
Later I became an emotional wreck and I now cry even at happy scenes, dang it lays on the ground What have I become.