Why is DBU the most popular base with an amidino group? Does the basic strength have something to do with the ring size being 7 for one of the rings?
DBU is a popular amidine base because it can be deemed to be of lower nucleophilicity than cheaper amidines e.g. formamidine.  It has been sometimes erroneously labelled as "non-nucleophilic" but seeing as it reacts with carbon dioxide and sulfonyl halides and anhydrides,  this cannot be supported. As has been pointed out, the price of bulk chemicals such as caprolactam (made from cyclohexanone which in turn comes from phenol) and acrylonitrile makes DBU accessible.
The 7-member ring structure isn't special per se but assists with steric bulk to reduce nucleophilicity of the free base and increase the nucleophilicity of the counter anion when acting as a (large) amidinium ion. This occurs through a reduced association of the ion pair.
For cost weighed up against basicity,  tetramethylguanidine is better value as an organic base if the extra strength is required.