Community detection in multiplex networks is a challenging task due to heterogeneous layer structures, weak inter-layer consistency, and noisy relations. The main objective of this study is to design an effective community detection framework that can adaptively exploit layer-specific information while preserving meaningful global structures across layers. To address this problem, we propose a new method named MLGFA, which integrates multiview layer-specific GraphFormers-based embeddings with heuristic layer weighting and label refinement strategies. The method first obtains expressive node embeddings for each layer, capturing both local and semi-local structural patterns. Then, an adaptive layer weighting mechanism is applied to quantify the relative contribution of each layer during node similarity computation. Finally, a deep learning-based boundary node reassignment process is employed to refine ambiguous community labels. The proposed framework by combining heuristic initialization, transformer-based representation, adaptive layer weighting, and deep filtering of the detected communities provides an efficient approach for identifying community structures in multiplex networks. The proposed framework is evaluated on several real-world and synthetic multiplex networks generated using the LFR benchmark. Experimental results are compared against several state-of-the-art methods, including GenLouvain, Infomap, MDLPA, LCDMN, MVGL, MPBTV, DGFM3, and LART. The results show that MLGFA consistently achieves higher or competitive performance in terms of NMI and ARI, especially under high mixing parameters. For example, obtained results on multiple real-world and synthetic multiplex datasets demonstrate consistent improvements over the best competing baseline methods, with relative NMI gains ranging from 0.26% to 122.81% across real networks and from 9.23% to 22.04% on LFR benchmarks. This indicates the high capability of MLGFA in extracting the structure of real communities in multiplex networks. The source code is publicly available at: https://github.com/phdutm2009/Multiplex-Community-Detection.