Dysarthria severity assessment traditionally relies on time-intensive perceptual evaluation by Speech-Language Pathologists. This work presents a parameter-efficient approach for automatic severity classification on the HeyJay! dataset. A frozen wav2vec 2.0 backbone is paired with a lightweight MLP-based decoder incorporating learnable layer weighting, temporal attention pooling, and a compact embedding network. Under speaker-independent five-fold cross-validation, the system achieves 64.6% utterance accuracy, 61.2% weighted F1, and 80.2% speaker-level accuracy via majority voting. Learned weights reveal that upper Transformer layers (17--21) are most informative for severity discrimination. Error analysis shows that 80.3% of errors involve adjacent classes, with 62.1% concentrated at the Moderate--Severe boundary, matching the 62.5% inter-rater disagreement observed among expert SLPs at the same threshold. These results establish a first baseline on this dataset.