It is certainly possible to lose fat without losing weight. It is much better to be up 20 pounds of muscle and down 10 pounds of fat (Net: +10lbs) than to just do nothing and weigh a bit less.
If you feel better and look better, you're doing the right thing. I'm in a similiar boat as you, I was 5'9" 170lbs, started cycling, after one month I was down to 160, after two months I was back at 170 but with a lot more tone and a lot less gut.