It does have an effect. Its most noticable in Simulator at high tiers, where planes guzzle fuel like its soda. Youll see that once you land, your suspensions will drop down as soon as fuel is loaded, and then once more for weapons.
Fuel being weight is pretty easily noticeable. The real question is if cannon ammo also is weight, and if so, if weight is modeled per round or for the whole belt. Many times when limping back to base, with just a few remaining ammo, I wonder if shooting it out will help, or just make me slower due to recoil.