Average Weight of Weighted Average

Question

Assume we have for a series $x_k$ with $k=1, ... n$ the following weighted average given $$\frac{\sum_{k=1}^nw_kx_k}{\sum_{k=1}^nw_k}.$$ How could I calculate the average weight? My first approach would be the ordinary mean. However, this seems inappropriate to me because if any $w_k$ would be zero, it shouldn't contribute to the average, actually. Should I use for the weights as well a weighted mean, weighting the weights by themselves? Like this: $$\frac{\sum_{k=1}^nw_k^2}{\sum_{k=1}^nw_k}.$$