With the introduction of QUIC, a modern transport-layer network protocol, HTTP/3 leverages its benefits to enhance web content delivery. This paper proposes a mechanism based on the recently standardized Extensible Prioritization Scheme (EPS) for weighted incremental web content delivery. The mechanism augments the sequential scheduling to provide incremental and weighted incremental resource delivery. An existing HTTP/3 implementation was extended with the proposed mechanism and tested with the content of eight popular websites. The results of our experimental analysis show that weighted incremental prioritization improves Quality of Experience (QoE) as measured by Lighthouse, a standard QoE test tool. While overall improvements were generally achieved, we also observed a few cases where the performance degraded slightly, highlighting that the QoE is sensitive to factors such as web page structure.