The Weierstrass p has a strong similarity of the [p in the Sütterlin Alphabet](https://en.wikipedia.org/wiki/S%C3%BCtterlin), which had been developed in Prussia and, as Weierstrass worked in Berlin (the capital of Prussia), it may well be, that that is the origin of the letter. Books were printed in [Fractur](https://en.wikipedia.org/wiki/Fraktur), where the p looks quite "normal", i.e. quite different from a handwritten Sütterlin p which could explain, why it hasn't been replaced in the publication of Amandus Schwarz. But I am not a historian, so this answer is a bit speculative, albeit reasonable.