Is it something they are born with or is there an explanation at all?
This does contain manga spoilers, just to inform the people who've only seen the anime.
The first Demon Weapons were created 800 years ago prior to the start of the series, Arachne following instructions found within the Book of Eibon. To create a Demon Weapon she murdered a Witch to use as a sacrifice. Using the Witch's soul, which has the power of transformation, Arachne joined together an inanimate weapon and a human soul to create a Demon Weapon which had the ability to transform from Human to Weapon form. This act of killing a witch made every witch want to kill Arachne and demon weapons alike. One of the very first Demon Weapons to have ever been created by Arachne is suggested to be Giriko. The Demon Weapons, despite their unplanned creation, were accepted into the world, and the Eight Powerful Warriors were the first people to fight as Weapon and Meister teams.
The blood of a Weapon is passed down however depending on the circumstances of an individual's life that blood may or may not actually be awakened. There are families like the Nakatsukasa clan which are made up entirely of Weapons and families like the Evans family where the Weapon Soul is apparently the only member to have inherited the Weapon blood for numerous generations.
Source: Soul Eater Wiki: Weapons