"Do you ever stop trying to go heavier?"
I think Tik, Ilene, and JC summed up what "going heavy" means, but I want to add to the second question. It depends on your goals and what you want your body to look like. When I worked my way up to my now infamous 305# squat, my quads and hamstrings became proportionately too large for the rest of my body, especially because my calves refuse to get bigger. So I've lightened up and increased repetitions on quad exercises. (Don't scream- this is bodybuilding heresy!) The result is a leaner look for me. I seem to be able to build quad muscle indefinitely. However, that hasn't proven true for the rest of my body, so I'm still increasing weight on just about everything else. My muscle don't seem to be getting any bigger anywhere else except maybe my pecs and back, but they haven't reached my personal "too big" point yet.
When I was squatting heavy, I did feel like I was approaching the load limit for my joints. I think I'm 1/2" shorter
Mel