It's hard to answer whether your feeling "fat and weak" is an objective assessment or a subjective/psychological analysis. Your weekly exercise routine is certainly more fitness-inducing than some of my own clients (as a sports massage & nutritional therapist), but if you are eating more calories than you burn, no matter if those are healthier calorie sources than the average diet's, you will store fat. On the other hand, if you are not eating enough calories to fuel your daily and weekly expenditure/exercise, then you can certainly feel weak.
Improper breathing is one thing that can make an otherwise fit person perceive themselves to be unfit. You might want to ask yourself if you are breathing fully and properly during your exercise (or for that matter, throughout the day) to get the most out of it and to improve health markers overall:
1) "We breathe oxygen into the body from the atmosphere. While this oxygen does not itself contain useable energy, it is the key that unlocks the energy stored in previously-ingested food..."
2) "Learning to breathe during exercise has benefits such as preventing dizziness during activity, improving athletic performance, and increasing fat burning...."
And also, if you spend a lot of time hunched over or in otherwise awkward positions for your body while gaming or even while cycling, you may want to think about your posture and the suppleness and flexibility of your spinal muscles. Improper posture affects proper breathing (and all the concomitant issues with exercise and health noted above), and can contribute to a general daily feeling of being less than well or not at one's best:
3) "Bad posture is a modern day health epidemic that is much worse than most people naturally assume... One of the worst types of health problems people experience is a loss of the natural curves of their spine."