Basilisk weeds appear to have been modified in two ways: they grow quickly and reproduce in great numbers, and they grow in ways that create basilisk hacks. Every aspect of their forms, from the veins in their leaves, the fractal patterns of their branches, the flow of their bark, and even the sound of wind through them, has been engineered to erode human minds. Basilisk hacks are precise things, however, and the basilisk weeds don't always grow in quite the right way to produce their full effect. Often, basilisk weeds simply induce a feeling of vague dread, anxiety or confusion.
The majority of the basilisk weeds were, and perhaps are, on Earth. They would grow in terrible groves the locals learned to avoid, or else those wandering into forests would become confused, disoriented or catatonic, and never come back out.
Whenever a character views a basilisk weed, flip a coin. Heads, the character simply feels a sense of dread, tails they are effected by one of the incapacitating input type basilisk hacks.