Realization of quantum photonic devices requires coupling single quantum emitters to the mode of optical resonators. In this work we present a hybrid system consisting of defect centers in few-layer hBN grown by chemical vapor deposition and a fiber-based Fabry-Perot cavity. The sub 10 nm thickness of hBN and its smooth surface enables efficient integration into the cavity mode. We operate our hybrid platform over a broad spectral range larger than 30 nm and use its tuneability to explore different coupling regimes. Consequently, we achieve very large cavity-assisted signal enhancement up to 50-fold and equally strong linewidth narrowing owing to cavity funneling, both records for hBN-cavity systems. Additionally, we implement an excitation and readout scheme for resonant excitation that allows us to establish cavity-assisted PLE spectroscopy. Our work marks an important milestone for the deployment of 2D materials coupled to fiber-based cavities in practical quantum technologies.