Thanks everybody for the input.
I can see two explanations listed : mental or physical.
I would rather opt for the mental explanation because this never happens when I'm sitting around all day long at home.
I fly for a very large operation with routes all over Europe (just on my type), but for personal, quality of life, reasons I signed up for an option with very few routes that I end up knowing by heart. It's a bit boring to fly always the same route. Even going everywhere in Europe it would just mainly be sit around waiting (at least for the flight).
I never regret my choice of working in the airline because it's still my dream job, the quality of life and the technical aspects suit me very well, but I just don't understand why the boredom has a physical expression.
On a typical day, I will try to be on my phone as much as possible between flights as I feel it helps me unwind, but maybe it's a wrong impression and I should try stopping.
Or, maybe the other explanation is a bit of mental pressure (even if bored, one has to be able to react if anything goes sideways), and/or the pressure (my airplane goes up to 5000 to 8000ft cabin altitude depending on the flight). The real boredom comes from flying 4-leg days. On the last day of a 4-5 day shift, sometimes I don't even remember if I did the departure briefing.
About the physical side, for context I am 28, rather slim but I don't work out or do sport really regularly. I still live a somewhat active lifestyle. For example just this week I spent two entire days out, walking, shopping, sightseeing.. I ran with my sister's dog. I often walk instead of taking the tube, even up to 2-4km depending on the time on my hands. I have a two story apartment and often forget things downstairs or upstairs... My girlfriends keep me very busy as well.
I try to avoid eating bull!!!! all the time (which is difficult because our colleagues bring us exactly that) but I'm not very keen on it so still end up for example ordering desert at a restaurant and I don't always turn it down at private dinners.
I put on some weight last year (1-2kg) when I decided to eat more and work out at the same time (to gain mass), part of it should be muscle and part of it fat.. I looked very slim and wanted to diminish that (my BMI is between 20 and 21).
My favourite drink at work is tea, I try to avoid hot water as I was told they don't clean the hot water tank, but still take some hot tea sometimes. The rest of the time, I put one tea bag and keep it in my glass with cold mineral water for 4-5 hours, only before 4pm. After that time I will tend to drink cold herbal tea (no caffeine).
I don't like coffee. I will sometimes ask for a coke which has the caffeine, but try to avoid it for sugar reasons, just like apple juice. Tomato juice is a drink of choice because no sugar.
Regarding sports, I could do more, I admit it could have some benefits. Last time I tried to motivate myself to do sports, it lasted for 3-4 months only, then I stopped for different reasons. I usually jog around my home, I have several loops between 1-3km. I bought some very good shoes for skydiving but I don't really intend on doing many more jumps (I did seven, until the first solo flight) because of it taking a lot of time, and the activity not being very rewarding for a beginner. I could use these shoes for jogging, which would help me greatly reduce the risk of any pain (which would come automatically if I jogged to much with bad shoes).
I also wanted to work out but I durably hurt my elbow and stopped immediately (I have a little pain in the elbow when doing pull ups, which I think is preventing me from lifting weights...) I should maybe go see a sports doctor to ask why the pain isn't going away and how to lift weight.
From a health point of view, is it better to work out or jog ?
From a fitness (esthetic) point of view, I think the best is to work out 100% first to gain mass then jog to eliminate the fat, but it's very demanding to do so at a good level. I also bought 4000€ of measure clothing, so it would be a bit stupid to put on a significant amount of weight (be it muscle or fat) and having to throw away the brand new suits and shirts...
But it seems to take a long term dedication that I will never have.
Finally, regarding my sleep patterns, I am a late owl. So when on my own, I will sleep typically from 3 to 12 (9 hours), and maybe from midnight to twelve if very tired from an early wakeup. When I have an early wakeup from home, I have trouble sleeping before midnight, so I typically end up sleeping 4-6 hours before my first day. If there is a second early, I will have much less trouble sleeping early and try to have at least 6 hours if there is no third early, 7 hours if there is. And 8 hours if there is a fourth early (even if it means going to sleep at 8pm without eating)
I don't work for a very demanding carrier, I work airline but no more than 13 days per month. I can't say I'm overbooked. If I worked 18 days (the maximum) I would make 30% more as well which would be very motivating.