Generative AI model outputs have been increasingly evaluated for their (in)ability to represent non-Western cultures. We argue that these evaluations often operate through reductive ideals of representation, abstracted from how people define their own representation and neglecting the inherently interpretive and contextual nature of cultural representation. In contrast to these 'thin' evaluations, we introduce the idea of 'thick evaluations:' a more granular, situated, and discursive measurement framework for evaluating representations of social worlds in AI outputs, steeped in communities' own understandings of representation. We develop this evaluation framework through workshops in South Asia, by studying the 'thick' ways in which people interpret and assign meaning to AI-generated images of their own cultures. We introduce practices for thicker evaluations of representation that expand the understanding of representation underpinning AI evaluations and by co-constructing metrics with communities, bringing measurement in line with the experiences of communities on the ground.