It seems like we have maybe a dozen regulars here in meta. The vast majority of the main site's users never seem to come here or participate here. What can we do to get more participation on the meta site?
Well, your chatroom is really active, and growing moreso every day. During the group-watches (as "commercial breaks" or the like) make a plug for users to get more engaged in the site by participating in the meta -- mention any ongoing contests or giveaways that may be going on. Also consider selectively posting meta questions into the chatroom from time to time; this way, really important site issues will get some visibility without cluttering the chat with a constant feed of, "Why is my question closed?" as metas will often have. (Pasting question into chat worked in DIY, where the meta activity spiked when we started posting in meta questions that we felt were Relevant to Our Users' Interests into the chat directly. I believe DBA does something similar, as well.)
Now that you're a graduated site, you should have access to the Community Promotion Ads. Consider submitting one either to promote a specific giveaway/contest or to just encourage meta participation all around.