Just as നെയ്യ് comes from the Sanskrit സ്നേഹം, the word for fear, പേടി comes from the Sanskrit ഭീഷ് (meaning fearsome). (Such words are called തത്ഭവം )
That might sound like a far cry. But it is not that difficult to see. It is conceivable that ഭീ was transformed to പീ. What about the ഷ? There is this etymological rule that in some words the ഷ gets transformed into a ട. Thus, ഭീഷ് -> പീട് -> പേടി.