Racket weight is normally measured in grams and standard weight of a typical standard racket is between 80 and 95 grams (although there are some rackets which are lighter or heavier than this range). The weight is measured BEFORE stringing. 84-85 grams is normally considered as the medium weight for most players, where it’s not too light or too heavy. Anything lower than that is considered light whereas anything higher is considered heavy (please take note that this is just a general statement, every player has different strength and hence the classification of heavy or light is absolutely subjective).
A heavier racket will obviously give you better power and it also vibrates less when you hit on the shuttlecock. On the other hand, a heavier racket obviously reduces the maneuverability of the racket.
The weight of a modern badminton racket is normally mentioned in ‘U’ specification. One important point to take note at is that a same racket model could come with different weight variants to suit the needs of different players.
There is no fix rule on racket weight selection as it really depends on your strength and also your style of play. As a general rule, if you have enough strength, you could get yourself a heavier racket if you wish to have the extra power out of it. However if you need fast racket actions, for example if you are a front court player in doubles, then get yourself a lighter racket for the maneuverability. BE CAREFUL not to get a racket heavier than what you could handle as it might increase the risk of injury to your wrist, elbow and arm.