The nickname "burger" is matching pretty well indeed. I recently had the chance to try on the "double burger" 5004 of a friend. Both models have a similar charm to them.
Compared to my larger 5270 the smaller size of the 3970 makes the look more dense and very appealing. The thicker proportions making it very special in my eyes.
For that reason I also love my Rolex Pre-Daytona 6234 which is also 36 mm in diameter and thick like a little burger. But of course 3970 and 6234 are past comparison.