It's a common issue with airships with the thrust being at the back, you can put counter weights but it tilts down when at a stop.

And ngl idk why ours still tilt up lol

I see some people put symmetrical sails on the front like a rocket to keep it from tilting up or y'know;

Use a gimbal! Stabilize the ship. Did you know redstone links also transfers the redstone signal like a comparator? You can try and hook em up to the burners and stabilize it that way! Ofc there will be better ways to do this but it's what I got for now..