When used repeatedly, weapons will deteriorate and eventually become unusable.
Durability is tracked by a star in the corner of the weapon icon. Each time the weapon is used, there is a chance that it will lose a level of durability, which is depicted by a portion of the star turning from yellow to black. Every weapon has five levels of durability from undamaged to broken. The likelihood of dropping a level of durability depends on the particular weapon (for example a spiked baseball bat is more likely to become damaged with each hit than a regular baseball bat).
When the final level of durability in a weapon is reached, the star loses its final sliver of yellow, turning completely black. At that time the weapon remains equipped, and can still be brandished, but it will not function as a weapon (e.g. a bat cannot be swung, nor a shotgun fired). The weapon will show a red cross next to its icon to denote that it is broken and can no longer be used.
Some weapons that have been used, but are not yet broken, can be repaired.