From a more practical standpoint, many weapons have some weight to them (at least the original steel ones did, unlike some modern day "wu shu weapons") and practice with them develops the body in a way that empty hand work alone cannot. Some weapons develop certain parts of the body more extensively than others. For example, the staff and spear develop the waist and legs. The arms alone are not sufficient to power these long weapons.
Because many weapons move at greater velocities than the body alone, eye-hand reflexes and coordination are developed to a greater extent than would be possible with empty hand training alone. This is one of the benefits of two-person weapons forms where students must react to weapons coming toward them. The psychological toughness of dealing with weapons transfers to empty hand situations. If one can face a weapon without fear, fists and feet do not seem very threatening.
The techniques used in many classical weapons forms often translate directly to objects that may be available for use in a self-defense situation. A belt or dog leash may be used like a chain whip or rope dart. A stick or broom may be used like a sword, a pair of scissors like a dagger, etc. Actually, many classical weapons were originally tools that were adapted to combat.
Many benefits may be gained from training with martial arts weapons; however, when it comes to self-defense, the bottom line is: the best weapon is a firearm. If you live in a state that has concealed carry permits and you qualify for one, the best defensive weapon is to carry a concealed, readily accessible semi-automatic pistol.