Can gaining too much muscle mass have similar health risks as being obese?

No: Obesity is much more dangerous. It is good that you are conditioning which also gives you cadiovascular safety. Obesity causes cardiovascular diseases like heart attack, hardening of the arteries due to cholesterol build up in your blood vessels - called atherosclerosis or strokes. That is why obesity is a killer. Importent here is you heredity also You can discuss this with your physician.