Chances are that calculators that are taking into account your weight are using the MET method of calculation, which I think is highly dubious in estimating individual calorie burn. MET assumes a very direct relationship with weight and the number of calories burned that I believe is problematic when analyzing the use of a machine whose primary mechanical function is supporting your weight and propelling it efficiently. Frankly, I find it impossible to believe that the relationship between weight and calorie burn is the same for cycling as it is for running, so I strongly suspect that MET tends to overstate the calorie burns for heavier cyclists, and the heavier you are, the higher the overstatement.
I lost about 140 pounds over 3 years about 6 years ago. I lost the first 100 pounds pretty much through diet alone, then lost about another 54 pounds through intense exercise while actually eating more, but that's only with about 12-15 hours of relatively intense riding/working out per week. It's not a regimen I can recommend to anyone because it's a very large time and energy commitment that probably can't work for many people. I don't tell people what I think they should do because I don't really believe anyone is particularly good at giving such advice. There's simply no scientific evidence that anyone has come up with a specific program that people can and do successfully follow consistently. I developed what I do to keep the weight off for the past 5 years through trial and error.
I will say that I think there probably needs to be a mix of calorie control and exercise to successfully lose and keep off weight, but I think the balance of those and what foods work best vary immensely from person to person. I will also say that nothing makes me hungrier than lying around, doing nothing. I end up cooking and eating just for something to do.