The "aerobic fat-burning zone" is a myth. While it's true your body will burn a higher percentage of fat at a lower level of effort, you'll burn less overall calories than if you ride at higher intensity. For weight loss, it's total calories burned that's important (regardless of whether you're burning more fat or carbs).
That said, you can't ride at 100% intensity for very long, so you need to find a good balance...basically, if you're going for a long ride, you find an intensity level that you can hold throughout the ride.
But, if you can't go long, go hard. You'll burn more calories with the time you have available.
As for "eating as much protein as possible"...that's not very smart. For cycling, you need carbs to fuel your efforts. Better to eat a balanced diet of carbs, fats, and protein (perhaps with a slight emphasis on protein, especially if you're lifting weights).
For weight loss, quit drinking your calories (no sodas, juices, etc., and cut way back on alcohol). Also, cut back on food portion sizes (hint: if you go out to any restaurant in the US, and clean your plate, you've not "eaten", you've "overeaten").
Bottom line: eat a little less, and move a little more. If you can figure out how to burn a few hundred calories each day more than you eat, you'll lose weight. It's not rocket science, but it does take work, and persistence.
Best of luck.