Almost everything the medieval basilisk does was added after Pliny. The Natural History gives a creature about a foot long, marked with a white crown, that kills grass and cracks stone and is itself killed by the weasel, which is the one detail nobody dropped. Isidore of Seville carried the account into the Latin Middle Ages, and the bestiaries expanded it, because a bestiary entry has to teach something and a small poisonous snake teaches less than a monster.
The additions arrived in order. The killing look, distinct from the killing breath, became standard. The mirror trick followed, on the logic that a gaze that kills must kill its owner. Then came the birth story: an egg laid by a cockerel and hatched by a toad or a serpent, which made the creature an offence against natural order rather than merely a hazard. That last accretion is where the basilisk and the cockatrice become impossible to separate.
Early modern Europe kept the creature alive as a civic threat. A story of a basilisk in a cellar in Warsaw circulates from the sixteenth century onward and is repeated by later compilers, who are copying each other rather than reporting. Stuffed rays cut and dried into winged serpent shapes, sold as basilisks to cabinets of curiosity, are physical objects that survive in museum collections and are the closest thing to evidence the tradition ever produced.