Bezout's Theorem states that for two homogeneous polynomials $f(x,y,z), g(x,y,z)$ over an algebraically closed field of degrees $m,n$ respectively, such that the two polynomials do not share a common component, then the number of intersections of $f,g$ is equal to $mn$ counting multiplicity. Is there an analogue of this theorem for WEIGHTED homogeneous polynomials? That is, suppose that $w_1, w_2, w_3$ are three coprime positive integers, and for a given polynomial $h(x,y,z)$ let $e_1(h), e_2(h), e_3(h)$ denote the degrees of $x,y,z$ in $h$ respectively. We say that $h$ is weighted homogeneous of degree $d$ with weight $(w_1, w_2, w_3)$ if $h$ satisfies $w_1 e_1(h) + w_2 e_2(h) + w_3 e_3(h) = d$. If we allow $d$ to vary across all positive integers, then the resulting set of polynomials is the set of weighted homogeneous polynomials with weight $(w_1, w_2, w_3)$.
So my question is, is there an analogue to Bezout's Theorem in this setting? That is, is there a constant $W = W(w_1, w_2, w_3)$ which depends on $w_1, w_2, w_3$ such that if $f,g$ are two weighted homogeneous polynomials with weight $(w_1, w_2, w_3)$ with no common componets, then the number of intersections of $f,g$ is bounded by $W(w_1, w_2, w_3) \deg(f) \deg(g)$?