Alternative theory (without any data :)):
Perhaps most of the photos with 30 tags are dew to semiautomatic fill-all-the-keywords strategies in SEO attempts. So most of them have naturally more exposure than photo from individuals that only use a few tags (like “dog” and “sleeping”).
Then they get more likes because they have more traffic, not because they have more tags
Proposed experiment:
* Pick 70 new photos, and separate them in 7 groups of 10 photos at random.
* Post them with 0; 5; 10; ... ; 30 tags and wait ...
* Count the likes for each group
* Kill outliers? 10 is too small? Find someone with more knowledge of statistics to check the experiment.