I was delayed getting online today. I was feeling unwell. My apologies.
I would not be so quick to discount sleep apnea were I you. Of course online I cant say you have it, we can only make educated guesses based on what you wrote but it is possible. From what you describe, it is not quite "when you are awake"; its when you are "starting to fall asleep" and you may be in a state that is not full awakeness. When you awaken in the morning, you may be short of breath because you have not breathed well during the night and that explains that morning huge breath. And you do not know what your breathing is like while you are fast asleep.
Sleep apnea is not something that should be ignored, it is not benign. There are two types of it. One is obstructive and is when the airway is obstructed by tissue or constricted; the other is central and is a problem within the brain; it is not sending signals to breathe in sleep as it should. Both types are equally dangerous. The low oxygen levels of sleep apnea can cause high blood pressure, which can lead to an enlarged heart and potentially congestive heart failure (a problem with the hearts ability to pump); additionally people with sleep apnea are at increased risk of strokes.
You have risk factors for it. You are overweight which is a risk factor and you do snore; which can be a sign. Additionally, men are more likely to develop sleep apnea than are women, and so are those who are older.
I think this is definitely worth mentioning to your doctor, a sleep study is how sleep apnea is diagnosed, and there are methods of helping it. They can include special masks worn during sleep to oral appliances to weight loss.
Here is more information from the Mayo Clinic on this topic: http://www.mayoclinic.com/health/sleep-apnea/DS00148
I hope I was able to help,