Grading short answer questions automatically with interpretable reasoning behind the grading decision is a challenging goal for current transformer approaches. Justification cue detection, in combination with logical reasoners, has shown a promising direction for neuro-symbolic architectures in ASAG. But, one of the main challenges is the requirement of annotated justification cues in the students' responses, which only exist for a few ASAG datasets. To overcome this challenge, we contribute (1) a weakly supervised annotation procedure for justification cues in ASAG datasets, and (2) a neuro-symbolic model for explainable ASAG based on justification cues. Our approach improves upon the RMSE by 0.24 to 0.3 compared to the state-of-the-art on the Short Answer Feedback dataset in a bilingual, multi-domain, and multi-question training setup. This result shows that our approach provides a promising direction for generating high-quality grades and accompanying explanations for future research in ASAG and educational NLP.