I also have a perpetual hunger. I think it depends one a person's physiology and/or their eating habits:
Because I am always hungry (= peckish for a bite) I have to watch myself, because it is very easy to succumb to desire and eat until I feel a bit bloated. That is too much, so I have to decide to eat a small amount more often. Like at work, I have a tub of yoghurt mixed with muesli, 2 fruits, 2 sandwiches and 2 eggs, and I spread those over the entire day, eating perhaps 1 item per hour. I never feel really really hungry if I do that.
At home, I have a normal meal at evening, then at night 2 more small meals. It is during the late night that I have the most problems, since I don't have a set habit like in daytime, and I may gorge on biscuits if I don't watch it. That happened last night again, with me feeling guilty so this morning on my commute I took my mountain bike and rode to work on soft tires.
Since I started commuting, I eat more obviously because I need more.
So, in your case, if you keep up your cycling, you will need more because of that, but also because of your metabolism is now likely to be at a higher level than when you were overweight and unfit. So no problemo, eat away, but try to find a habit so that you don't gorge yourself at night. This way you will easily find a level which suits your particular case for constant weight.
Disclaimer: I'm not an expert. I learned this during my own (35 puny pounds) weight loss.