In this document we study the application of weighted proportional fairness to data flows in the Internet. We let the users set the weights of their connections in order to maximise the utility they get from the network. When combined with a pricing scheme where connections are billed by weight and time, such a system is known to maximise the total utility of the network. Our study case is a national Web cache server connected to long distance links. We propose two ways of weighting TCP connections by manipulating some parameters of the protocol and present results from simulations and prototypes. We finally discuss how proportional fairness could be used to implement an Internet with differentiated services. 1 Introduction 1.1 Fairness Fairness is among the most important properties of data flows in the Internet. Fairness implies that whenever there is congestion at a bottleneck, each flow going through that bottleneck gets a fair share of the available bandwidth. TCP flo...