 B2 adjoint representation weight diagram

For simple roots $(1,0),(-1,1)$, Dynkin labels of a Euclidean weight $(x,y)$ are $(2x,-x+y)$. The highest root $(1,1)$ gives the Adjoint representation, of dimension ten. Its eight nonzero weights are the eight roots of $B_2$; the zero weight has multiplicity two. The nine distinct label pairs are $(2,0),(0,1),(-2,2),(2,-1),(0,0),(-2,1),(2,-2),(0,-1),(-2,0)$.