Static vs Dynamic Balancing
Most propellers, especially those with a TCDS i.e. Hartzell, McCauley, will be static balanced on a static balancing arbor prior to leaving the MFR.
Most prop shops will check the static balance of the prop after an IRAN or overhaul.
This helps get the prop hub and blades into a known "in-plane" mass balance condition.
In plane axis is spanwise to the blade, out or plane is perpendicular to the spanwise axis of the blade.
Rotorcraft folks will know this the Vertical and Lateral axis.
Static balancing on an arbor typically does not include the spinner or mount plates / hardware.
The prop hub and blades are also typically checked for blade track and angles to ensure the blades / hub meet the static blade track and angle requirements for the prop.
Once the prop is reinstalled on the engine and run, it requires Dynamic balancing to take into affect the mass imbalance (aka vibration) caused by centrifugal forces.
Note - Dynamic balance of the prop only addresses "in plane" mass imbalance, if there is a out of plane vibration, adding weight will not solve it.
There are several items that can cause a perfectly static balanced prop to exceed the dynamic balance limits, which are "typically" 1.0 IPS.
If the crankshaft is bent or one blade is bent / out of track, it will cause the entire prop to "wobble" enough in the out of plane axis that it will be hard to dynamically balance, if not impossible.
Typically all the blades have the same chord and spanwise profiles, however if one blade has been repaired, it may produce more or less thrust than the other(s) and this will result in a out of plane vibration (aka a thrust imbalance) which cannot be dynamically balance with weight alone. Prop overhaul shops check this as part of an IRAN / Overhaul, so it shouldn't be an issue...unless Bubba had filed the heck out of one blade to remove a nick / gouge.
If the either the spinner or mount plates have excessive mass imbalance, it can create a situation where a perfectly static balanced prop cannot be dynamically balanced because the entire prop, spinner and mount plate assembly is spinning as a "total mass".
You can check the static balance of the spinner / mount plates using a bubble balancer and add / subtract weight as necessary to get a decent static balance before attempting dynamic balancing.