Weak weak approximation and the Hilbert property for degree 2 del Pezzo surfaces

We prove that del Pezzo surfaces of degree 2 over afield 𝑘 satisfy weak weak approximation if 𝑘 is a number field and the Hilbert property if 𝑘 is Hilbertian of characteristic zero, provided that they contain a 𝑘-rational point lying neither on any 4 of the 56 exceptional curves nor on the ramification divisor of the anticanonical morphism. This builds upon results of Manin, Salgado–Testa–Várilly-Alvarado, and Festi–van Luijk on the unirationality of such surfaces, and upon work of the first two authors verifying weak weak approximation under the assumption of a conic fibration.