Why do my gums stick out so much?

Be careful what you wish for! Your gums are extra thick because the underlying bone is thick. You have what is called a thick boney type. The gums get their health from the bone. With the thick bone you are unlikely to experience receding gums. Remove some bone and you might cause recession in the gums. Personally I think you have a very attractive smile. Lessening the overjet will make it even better. If you are still not satisfied, you might consider lengthening your teeth by removing some bone vertically, not horizontally. This is most easily accomplished by using an erbiuim laser manufactured by Biosase.