I actually have a Gretsch Junior. Its body feels really small, like a vintage Les Paul Jr. I had back in the day, And, yep, no neck dive with it, but then again, there isn't anything of substance in the headstock to cause that.
I've also played a Danelectro Longhorn. Weird-ass body but minimal headstock. And the neck seems to go on forever. I sold it years ago, but I do miss it. It played well and was very balanced while standing and playing.
Before that, I had a Rickenbacker 4001. Beautiful axe and very substantial in the body. I don't recall any neck dive with it.
These days, and since playing the Danelectro, I prefer short scale basses. The ease of making stretches, the less weight, and the lower string tension are all pluses to me. I dig the tone, too. So, I've got a SBMM Stingray Short Scale incoming tomorrow and a Chowny SWB-1 coming in a few weeks. Yeah, I dig shorties.