MOTIVATION: Multiple sequence alignment (MSA) remains a core problem in bioinformatics, yet most widely used alignment methods still rely on static amino acid substitution matrices that cannot adapt to sequence-specific context. RESULTS: BABAPPAlign is a progressive MSA engine that replaces static substitution scoring with a trained residue-level scorer operating on fixed protein-language-model embeddings, while retaining exact affine-gap dynamic programming. It also provides an integrated codon-aware alignment mode. Using BAliBASE as the primary inferential benchmark, with supporting external validation on deterministic subsets of PREFAB and HOMSTRAD, the learned backend outperformed matched in-engine EBA-style cosine and BLOSUM62 controls, and also exceeded MAFFT. AVAILABILITY AND IMPLEMENTATION: BABAPPAlign is implemented in Python and distributed as an open-source command-line package through PyPI; the source code is available at https://github.com/sinhakrishnendu/BABAPPAlign, the archived software release is available at https://doi.org/10.5281/zenodo.17934124, and the pretrained model weights are available at https://doi.org/10.5281/zenodo.18053200. SUPPLEMENTARY MATERIAL: Supplementary material is available at Bioinformatics online.