We might simply be getting into semantics here,
Of course! - This
is a technical forum, not a layman's forum.
but an observer on board a turning aircraft feels an increase in force on the normal axis which is exactley the same as an increase in weight. From his frame of reference, his and the aircrafts weight has increased.
No it hasn't. The weight has remained the same, the observer is feeling the force which is accelerating them around the corner, in the same way that if you hammer the accelerator in a car you feel the back of the car seat pushing you forward.