Unfortunately doing day passes at gyms can get expensive. I would check the cities you are traveling to and look for any chain gym you might be able to join that has locations across Europe.
Traveling and exercise that even more dedication than being at home. If you can't realistically get to a gym invest in things like bans and other items that you can use your own body weight. Go for a walk or a run. Use steps, walk fast and walk on the people movers. In short find ways to increase your phyiscal activity.
Also, diet. Again its tough. Airline food, even the stuff up front, is horrible as is much airport and hotel food. Try to find a grocery store in your locale area or places that serve healthier food. Avoid excessive amounts of booze. Avoid the deserts and ask the FAs to serve you salad without dressing.
If you don't change this in your 30s within five years most of your weight gain will be permanent. Take a look around at some of the 40 and 50 somethings you see traveling (most of them that can barely fit into a business/first class seat) and decide if you want that to be your future.