apologies, but sloppy terminology. In a turn an aircraft experiences a load factor greater than 1 (centrifugal acceleration) ... not quite the same as "weighs more".

So the airplane is turning along an arc. centrifugal acceleration is radially outward, and weight (1g) is down). These are balanced by the lift force, normal to the wings (which are banked). It works out that a 60deg bank (to horizontal) means the lift force is double (to balance the vertical loads), ie a load factor of 2.

another day in paradise, or is paradise one day closer ?

Agree.

In other words: Normal (coordinated) banking results in a curved path. The curved path is a result of the additional centripetal force into the direction of the curve (to the middle). The pilot may have to apply more force to the stick, pulling harder. The wings will be more heavily loaded. The forces are perfectly real, and aircraft have limits.

Semantically, "weighs more" is normally related to gravity. But ask Einstein and he will tell you that gravity and acceleration are equivalent, in a very deep sense. Fundamentally, language hasn't kept up with the Physics, so semantic debates often become messy.

The grammatical explanations of centrifugal vs centripetal usage often happen to also contain excellent explanations of the Physics.

College physis course problems often called this "apparent weight",another common example being elevator problems.

Quote (rb1957)

that a 60deg bank (to horizontal) means the lift force is double (to balance the vertical loads), ie a load factor of 2.

Well, yes.

But frame of reference becomes important here.

Lift is defined in steady-level flight. Lift equal and opposite to weight.

But a banking aircraft is no longer steady-level.

So it's important to understand if you are speaking about an aircraft frame of reference or still a gravity frame of reference.

Pedantically, rb1957's statement should be " that a 60deg bank (to horizontal) means the lift force isthe force acting on the aircraft in the same direction that lift acts relative to the aircraft when the aircraft is in steady level flight is double (to balance the vertical loads), ie a load factor of 2."

But that's really tedious to type.

lift acts normal to the wings; if the wings are inclined (banked) then so to is the lift.

another day in paradise, or is paradise one day closer ?

Yes. With aircraft frame of reference.

But not the weight.

Frame of reference. This is what confused the OP.

https://books.google.com/books?id=GN93DQAAQBAJ&...

lift is normal, weight is down.

whether you draw the FBD sitting in the plane (lift up, weight banked) or from outside the plane (lift banked, weight down) it's the same.

I think what confused the OP is the sloppy terminology "weight increases", as though the weight vector increases.

another day in paradise, or is paradise one day closer ?