How do I calculate calories burnt using my bicycle's weight?
To be honest, you're really asking this question too late. If you had asked before your tour, I believe the easiest way you could have measured it would be to find a cycling app which takes your weight and your other physical information. Then you simply weigh your fully loaded bike and add that weight to your own, then the app would measure your total calories burned. (Even this would only be a rough estimate).

However, there is no solid answer to this question. As I said before, you would have been better off asking this prior to the trip, as there are dozens upon dozens of factors needed to give you an accurate BALLPARK of how many calories you've burned. (I.e. Speed, terrain, average gradient, food consumed while on your trip, average power output, length of time spent in the saddle, cadence, over all distance, e.t.c.)

I suppose if you wanted a very rough estimate, find a calorie calculator online, input the total weight, (you and the loaded bike), take the distance traveled, and the estimated total time in the saddle. This method would be fairly inaccurate, but without the factors listed above, I believe it's the closest you would get.