Actually weight over flat terrain has little impact. Speed has biggest impact on required power, due to air resistance. Which is why I quote it to illustrate my example. Fitness and height are irrelevant.
As we know from Matt that his speed is less, then it follows that his power output and therefore calories burned per hour will be significantly less than the 1000 calories this website blithely assumes. How much less I do not hazard to guess, and I am not advocating that he uses my assumption, as we know his route in the Downs is hilly.
As an additional pointer I also do cycle a lot in the North Downs, and my average speed there is in the 17 mph region, if that is of any use to the OP. This is for longer (cca 3 hour) rides, so will not be at the same intensity as the rides I referred to earlier.
My example is not misleading, as to whether it is helping, perhaps you should credit the OP with enough intelligence to decide for himself if it's helpful or not. Your advice to rely on inaccurate information, and to assume that he is burning a lot more calories than he is could be considered unhelpful by some
Not to mention your blind faith that his problems are due to his diet. He should go and see his doctor, and get a full bloodwork done in the first instance.