We talked about the Greek appreciation for large buttocks, but the Western tradition of favoring "fat-bottomed girls" went on long after. There were many copies of the Aphrodite Kallipygos in the Greek and Roman era (in fact, the oldest surviving version is a copy), and numerous copies have been commissioned in the modern era, especially in the 17th and 18th centuries. In the 19th century, a catalog entry for the statue notes that the buttocks are darkened because many people loved the statue so much they kissed its cheeks.
In addition to admiration of the Aphrodite Kallipygos, the popularity of odalisque paintings shows the affinity for buttocks. Commonly represented as lounging with their copious buttocks exposed and/or raised, the odalisque, a harem slave or concubine, became a popular image among painters of the 19th century. They even inspired a short-lived trend for Arabesque clothing among women considered "free-thinkers," sometimes considered demimondes.
So the "recent" trend toward appreciating women with larger buttocks is not actually recent at all, but, instead, is a continuation of a deep tradition. Larger buttocks are nearly universally praised.