Could Weeping Angels lurk proudly among Doctor Who's best ever villains. Resembling ordinary statues, the Weeping Angels send their victims to different time periods and feed upon the energy left behind. Strong enough to snap necks and impossibly quick, the Weeping Angels descend upon prey in the blink of an eye, but possess one crippling weakness - they can only move when no one's looking. So long as you keep an eye on them, the Angels are as harmless as church cherubs.
Doctor Who has kept the origin of the Weeping Angels frustratingly mysterious thus far. The creepy stone villains have no confirmed home planet, and even The Doctor doesn't know how old they truly are. Doctor Who has only revealed that Weeping Angels hail from the very beginning of time, and exist across all dark corners of the universe. Essentially, they can pop up anywhere, and in any given time period. The veiled history of the Weeping Angels has allowed for all manner of outlandish fan theories, and one of the most popular claims the creatures could be former Time Lords fallen from grace.
This idea began circulating after David Tennant's farewell story "The End of Time," in which Timothy Dalton's Rassilon leads the Time Lords to modern day Earth (where else?) as a means to escape the Time War. Their freedom would've wiped out all creation, but The Doctor and The Master team up to foil their corrupted kin. When Rassilon emerges from the Immortality Gate, however, he proclaims that two Time Lords opposed him, and must therefore stand in shame with their hands covering their faces "like the Weeping Angels of old." Apparently, Time Lord punishment means being forced to mimic a Weeping Angel, and this revelation triggered speculation that the two species were somehow connected.
Assuming Rassilon's punishment is some long-standing Gallifrey tradition, it seems that troublesome Time Lords throughout the civilization's history were made to cover their eyes and assume the position of a statue to atone for their sins. Staying that way for endless millennia, these fallen Time Lords might've gradually turned to stone, explaining how the first Weeping Angels came into being. Alternatively, Time Lord science could've been employed to deliberately turn sentenced criminals into ravenous time-traveling statues. This practice would be kept secret, of course, meaning The Doctor stays blissfully ignorant.
This ambitious theory would for why the Weeping Angels feed on time energy, and how they can send their victims through history. And after being transformed into monsters by their own race, it's hardly surprising that the Angels might become vengeful. The Weeping Angels being disgraced Time Lords creates a classic Doctor Who time travel paradox - the Time Lord punishment was inspired by the Weeping Angels, but the Weeping Angels were created by the Time Lords' punishment.
Time Lord chronology is complex enough without tossing killer statues into the mix, so Gallifrey almost certainly won't be behind the Weeping Angels' existence. But while the Angels' history goes unaddressed, their connection to the Time Lords remains a possibility; after all, even Doctor Who itself doesn't fully understand the biology of Time Lords. In a fascinating wrinkle to the theory, one of the two shamed Time Lords in "The End of Time" was later confirmed by Russell T. Davies to be The Doctor's mother. This means The Doctor's own parent could've been among the very first Weeping Angels.