Multipath QUIC (MPQUIC) enhances web delivery performance by enabling concurrent transmission across multiple paths. Despite its appeal, unresolved issues persist in the current MPQUIC specification. The congestion control in MPQUIC relies heavily on packet loss, favoring paths with lower drop rates. This proves to be detrimental in heterogeneous wireless networks with frequent packet loss and varying path characteristics. Moreover, fairness principle limit its performance, especially in scenarios with independent paths. Besides, dynamic and asymmetric paths exacerbate challenges in packet scheduling, leading to potential out-of-order (OFO) arrivals and Head-of-Line (HoL) blocking. This paper introduces a novel scheme, Bottleneck-fairness and BBR-based Congestion Control (2B2C), inspired by Google Inc.’s BBR algorithm. It identifies subsets of MPQUIC’s subflows with shared bottlenecks based on BBR’s internal mechanism and dynamically adjusts the pacing rates to enhance throughput while preserving bottleneck fairness with single-path flows. To address the inter-stream and intra-stream HoL blocking, we propose a Priority-based Stream-aware Packet Scheduler (PS2) with a stream dependency tree structure, a priority-based queuing and a packet scheduler based on mixed-integer programming. Experimental results demonstrate that 2B2C achieves higher throughput with maintained bottleneck fairness, and PS2 effectively alleviates HoL blocking in contrast to state-of-the-art MPQUIC schemes over heterogeneous wireless networks.