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.