If I may echo some other posts..
What seems to give people difficulty with these sorts of problems and concepts is the need for juggling a number of different forces (external and inertial) acting in different directions to end up with an instantaneous resultant force which relates to what the mass is having done to it at that time. Very much like the navigation solution's vectors or the usually seen resolution of the wing's aerodynamic force vector into (vertical) lift and (horizontal) drag componenents.
Unless you need quantitative answers (ie numbers), forget the sums as that is an exercise in systems of units confusion. (Typically this causes undergraduate students the dickens of a problem for several weeks until they finally get their heads around systems of units and conversions. For the slower ones, like me, read months for weeks). Realistically, unless you are in the design or maintenance game, qualitative (ie a feel for the matter) probably is of more use than quantitative (ie numbers).
If I interpret the intent of the original post reasonably, the following may be of use -
In essence you have a number of major things going on, including ..
(a) weight acting downwards on everything, but the rotor blades in particular. This is no different to the sort of "weight" you see on the bathroom scales (the force the scales need to exert to stop you falling onto the floor) in the morning and accounts for the blades drooping at rest. The hub mechanisms prevent the rotors falling down to the ground. A bit like trying to hold your arms out horizontally for a prolonged period.
The suggestion that "weight" is no longer PC is a new one for me. I suspect that that comment related more to the use of the term in typical weight control calculations where "mass" would be more appropriate from a mechanics viewpoint. However, as we all know more or less what it is that we are referring to it really is an inconsequential consideration. "Weight", in the present case, merely refers to the forces arising due to the influence of gravitational attraction.
(b) a measure of engine-provided torque to drive the rotor assembly against drag forces, except in an autorotative state.
(c) as the rotor disk winds up, centripetal accelerations and forces act radially inward to keep the rotor going around in circles. Centrifugal reactions act radially outward. These terms often are used interchangeably in common discussion. This is a bit like getting a length of string with a lump of something on the end and spinning it around your head. The effort you put in to keep the lump from hurtling off into the darkness is the centripetal force needed to keep the lump going in a circle. The lump, meanwhile, continually tries to hurtle off into the darkness. This reaction to the centripetal force is normally given the term centrifugal reaction (more commonly, if less inappropriately, called centrifugal force).
(d) as the rotor winds up, the individual surfaces generate forces as they whizz around in the air - what we normally resolve in lift and drag components. We can ignore blade pitching moments for the present discussion.
As the rotor RPM increases the radial forces will tend to make the blades rise above their rest position. A bit like attaching a couple of pieces of string to a lump of something resting on the kitchen table. If we pull the two bits of string in different directions (weight and centrigual reaction directions), the lump moves in a third direction depending on the geometry and size of the applied loads. This latter direction is where the blade elements will sit.
When the pilot applies collective, however, the blade lift forces will make the blades move considerable higher and above the horizontal. The radial loads prevent the blades from rising to a level which would be other than useful.
(e) gyroscopic loads will complicate the situation when the disk is tipped.
Either way, the blades will end up doing whatever is appropriate according to the net effect of what all the various loads are doing.
Comparison of rotor disk and prop disk is complicated by the orientation and the quite different nuts and bolts mechanisms involved. However, in a similar manner, the prop blades are subjected to loads which tend to cause deflections similar to what is seen in a rotor disk.
In respect of your base question, the spinning mass isn't going to "weigh" less as that relates only to what the bathroom scales would read - which is near enough to constant for the range of heights we might be talking about. However, if you were to define "weight" as the tension load in the string which you are whirling about your head, then that "weight" would be very much increased, to incorporate the centipetal load component. LZ's numbers for a particular rotorcraft puts that bit into big number perspective.
These things are much easier to understand with a few models and pictures. Hopefully my attempt here hasn't needlessly complicated the matter.