We've discussed the kanji 津 before, when we did 津々浦々. It means "port," or "harbor," but remember: we also discussed how referring to multiple ports (津津) in an island nation lends itself to an idea all-encompassing "everywhere-ness." Maybe that has something to do with why 津津 can be defined as "being full," or "brimming," as it is here.
興味, as you probably know, is "interest," as in 「四字熟語に興味あります：I'm interested in Yojijukugo.」
1. highly interested
2. being immensely curious
3. with inexhaustible interest
The Japanese definition above specifies an interest that becomes more and more engaging the more you get into it, in a way that seems like it might never end.
Another good word to know in this case is 興味深い (きょうみぶかい；kyoumi bukai): of deep interest. So, "very interesting."
We'll have more in the way of antonyms next time!
There's intense curiousity about how the world of television dramas will develop from here on out.