We present a unified theoretical and observational framework reconciling recent prolific discovery of astrophysical anomalies by artificial intelligence (AI) with fundamental modifications to gravitational theory. Astronomers O'Ryan and Gómez employed the semi-supervised active learning framework AnomalyMatch to conduct the first systematic search of the 35-year Hubble Legacy Archive. In under three days, the AI sifted through nearly 100 million image cutouts (7-8 arcseconds each), identifying 1,300 confirmed anomalous objects, over 800 previously undocumented. These anomalies---gravitational lenses, violently interacting galaxies, ``jellyfish'' galaxies, and unclassifiable objects---represent a statistical treasure trove of non-standard morphologies and gravitational effects. We propose that a significant subclass of these anomalies, particularly those involving extreme lensing or dynamics in merging systems, are positive signatures of entanglement-driven gravity. This work rigorously derives the field equations of Entanglement-Weighted Operator Geometry (EWOG), a quantum-gravitational framework where spacetime geometry is an emergent operator expectation value weighted by quantum entanglement entropy. We prove that in regions of high entanglement flux---such as galaxy mergers or dense cluster cores---the effective gravitational constant $G_{eff}$ becomes a dynamic function of the entanglement weight $W(\mathcal{E})$. This leads to anomalously strong lensing, accelerated structure evolution, and morphological distortions aligning with AI findings. The synthesis provides falsifiable predictions for next-generation telescopes and a first-principles reason why AI mining of vast archives is essential for probing quantum gravity.