If you fill the cockpit with water, the pilot will feel a buoyant force. Humans have about the same density as water, so ignoring the scuba suit, the pilot will feel a buoyant force about equal to his own weight.
The plane's maneuvers don't change this result much. By the equivalence principle, when the plane accelerates, the water in the cockpit and the pilot both get heavier. The buoyancy changes in the same way the pilot's weight does.
If he feels weightless before takeoff, he'll continue feeling weightless during maneuvers. If he's supported by buoyancy before takeoff, he'll continue to be supported by buoyancy during maneuvers. (This assumes that the jerk, or time derivative of acceleration, is low enough that the water can remain in hydrostatic equilibrium during the maneuver.)
Although basic buoyancy works the same, there will be a pressure change during accelerations. If the plane is accelerating up at 9g, he'll feel pressure as if he's under water ten times as
deep as he really is dense as the water really is. As Bruce pointed out, this is a big pressure gradient, and the pilot will still realize that the force beneath him pushing up is stronger than the force above pushing down. He will essentially feel heavy.
Ignoring compression, changing Earth's gravity won't change whether something sinks or floats. Something more dense than water sinks. Something less dense floats. If we multiply gravity by some constant, an object immersed in water has the net force on it also multiplied by that constant. So if you have something that floats and has a net force on it of $1N$ upward under normal gravity, if you double the gravity, it will experience a net upward force of $2N$ and have double the acceleration (ignoring drag).