On a given pricing date t, the weighted-average yield curve  $//$ gives an idea of the risk free rates that have been used in discounting cash flows. Computation-wise, it is the weighted-average of the yield curves  $//$ used to discount the cashflows of each constituent i. For a single country index e.g. the UK index,  $//$ is the same as the yield curve for that country.
$//$ denotes the weight of constituent i at time t