Clique cover problem
I don't know if there is a suitable approximation algorithm for this problem, but I can provide a counter-example for your heuristic algorithm: 
Assume G has 2*n vertices with weights 
$$W(v_i) = w - \epsilon * i$$
Which in your algorithm will be sorted by this order:
$$v_1, v_2, ... v_{2n}$$
And there's an edge between $v_i$ and $v_j$ iff $\exists k : i-j = 2*k$
The resulting graph is the union of 2 cliques with size n
The algorithm alternates between these two, which means in every step a clique with exactly one vertex will be returned, yielding a final answer with weight:
$$2*n*w - \epsilon * n * (2*n+1)$$
But we know that the optimum weight is just $2*w - 3*\epsilon$ 
So the approximation factor can be as big as $n/2$ (assuming that the graph has $n$ vertices) which is not very interesting because the obvious algorithm "Pick each vertex as a clique" has an approximation factor of $n$