The locus of the vertices of quadric cones containing a set of six general points $Z$ $\subseteq$ $\mathbb{P}^{3}$ is a surface of degree four. It is known as the Weddle surface of $Z$ and it can be seen as the locus of points $P$ $\in$ $\mathbb{P}^{3}$ such that the projection of $Z$ from $P$ into a plane lies on a conic. Using this point of view, we generalize the definition of Weddle locus, $W(X)$, of a finite set of points $X$ by asking that the points in $W(X)$ project $X$ on some curves with "unexpected" degrees. This definition leads to several open questions, in fact even the dimension of $W(X)$ is unknown in general. In this talk, based on a joint work with L. Chiantini, L. Farnik, B. Harbourne, J. Migliore, T. Szemberg, J. Szpond, we will explore properties of the Weddle locus of finite sets of points and its connection with the WLP.