Before revision: Consider a frictionless market trading a finite number of co-maturing European call and put options written on a risky asset plus an instrument with path-dependent payoff known as a weighted variance swap, e. g. a vanilla variance swap or a corridor variance swap.
After revision: We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co-maturing European call and put options written on a risky asset plus an instrument with path-dependent payoff known as a weighted variance swap, e. g. a vanilla variance swap or a corridor variance swap.