While analysing challenges in pilot projects developing AI with marginalized communities, we found it difficult to express them within commonly used paradigms. We therefore constructed an alternative conceptual framework to ground AI development in the social fabric -- the Cloud Weaving Model -- inspired (amongst others) by indigenous knowledge, motifs from nature, and Eastern traditions. This paper introduces and elaborates on the fundamental elements of the model (clouds, spiders, threads, spiderwebs, and weather) and their interpretation in an AI context. The framework is then applied to comprehend patterns observed in co-creation pilots approaching marginalized communities, highlighting neglected yet relevant dimensions for responsible AI development.