The weapon of a specific style is usually very ornate or counter intuitive. The weapon will usually have a design which maximises its use with a specific power generation. Since this requires training from that style, it can be assumed that the weapon won't be taken away and used against the wielder. Often the weapon is so difficult to use that most people cut themselves just picking it up. Special training is often required just to be comfortable holding it. There are many examples of this on ebay. Many styles have unique variations on multiple weapons due to some unique training that they carry over into their weapon work.
Personally unique weapons are more difficult to spot Some styles have a high level form which uses a weapon attributed to one master. It is difficult to determine if they are training one guy's weapon or if the whole style actually develops those skills. Swords are easier to spot. They tend to be obviously of a different manufacture, will have a name inscribed on it and very distinctive features to the handle. Usually the swords name implies its special purpose or "magical" ability. Some weapons also started as unique weapons and everybody adopted them. The Tiger Hook swords are an example of this. The Kwan Dao and ring daggers are other examples.