Generative AI has enabled novice designers to quickly create professional-looking visual representations for product concepts. However, novices have limited domain knowledge that could constrain their ability to write prompts that effectively explore a product design space. To understand how experts explore and communicate about design spaces, we conducted a formative study with 12 experienced product designers and found that experts -- and their less-versed clients -- often use visual references to guide co-design discussions rather than written descriptions. These insights inspired DesignWeaver, an interface that helps novices generate prompts for a text-to-image model by surfacing key product design dimensions from generated images into a palette for quick selection. In a study with 52 novices, DesignWeaver enabled participants to craft longer prompts with more domain-specific vocabularies, resulting in more diverse, innovative product designs. However, the nuanced prompts heightened participants' expectations beyond what current text-to-image models could deliver. We discuss implications for AI-based product design support tools.