Industries tend to be broad, while markets can be as specific as a type of product or a brand. Expand your search to the broader industry category if information is limited on your specific market. Emerging or niche industries also may not have a full profile/report.
Industry classification systems are created to promote data comparability. SIC and NAICS (both created by the US government) are the most widely used.
Most industry profiles in databases have information on market size. You can also use the Economic Census data.
It is not always easy to find market size information on a very narrow or specific industry/market. Look for mentions of it in articles or on the web. When all else fails, you may have to make an educated guess based on existing information.