In this paper, we present a distributed flow control scheme which achieves weighted max-min fair bandwidth allocation among all source-destination pairs on a per-aggregate basis within its network. The motivation behind the scheme is the absence of per-aggregate flow control in the current Internet, resulting in inability to enforce a certain fairness on source-destination flows. In our scheme, the distributed algorithm to compute weighted max-min fair rates is based on PI control in feedback control theory. We mathematically prove the asymptotic stability of the algorithm in presence of aggregate flows with heterogeneous round-trip delays. Through simulations we demonstrate the effectiveness of the proposed scheme in controlling per-aggregate flows.