If you mean dynamically balanced its easy enough done providing you've got the right gear. Basically what you need is to mount the prop on a shaft between to very freely rotating bearings. Then its just a matter of spinning the prop and record if it stops in different places each time (if it does it's in balance) However if it stops in the same place each time it's out of balance. As far as rebalancing goes it's best done by an expert. Why dont you contact T.W.Norris Ltd, Isleworth, I'm sure they would check them for you (at a price)
Propellors do not go out of balance unless they are damaged by hitting things. If the blades are true, and there is nothing more than minor scratching and knicking on the edges of the blades, then its fairly safe to assume they are still balanced.
If on the other you have had a mishap, and the blade tips are bent, broken or deformed by more than 5 cms or so, then they will need attention. having them repaired or re-set will restore balance.
It sounds as though you have a vibration problem? If the blades look to be in reasonably good shape, check that there is not wear in the shaft bearings. Try rocking the propellor on its shaft sideways and vertically. Any movement will result in vibration in service and means the outer bearing is worn. This is usually either a rubber 'cutless' type or a plain white metal bearing - both reasonably easy to replace. With the cutless type, ensure there is an adequate water supply through the bearing to lubricate it, or it will fail again very quickly.
There are several other more serious possible causes of vibration, like damaged shafts, engine mounts, misalignment etc etc, and which feel like an unbalanced prop.